The index theorem and the heat equation method /:
This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
|
| Schriftenreihe: | Nankai tracts in mathematics ;
v. 2. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schrödinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th. |
| Beschreibung: | 1 online resource (xix, 287 pages). |
| Bibliographie: | Includes bibliographical references (pages 279-282) and index. |
| ISBN: | 9789812810106 9812810102 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn505142671 | ||
| 003 | OCoLC | ||
| 005 | 20250103110447.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 010307s2001 si ob 001 0 eng d | ||
| 040 | |a CaPaEBR |b eng |e pn |c UBY |d OCLCQ |d N$T |d IDEBK |d E7B |d OCLCQ |d OCLCF |d OCLCO |d YDXCP |d OCLCQ |d AZK |d LOA |d JBG |d COCUF |d AGLDB |d MOR |d CCO |d PIFAG |d VGM |d OCLCQ |d WRM |d OCLCQ |d VTS |d NRAMU |d VT2 |d OCLCQ |d WYU |d STF |d M8D |d HS0 |d LEAUB |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLCQ |d OCLCO |d CLOUD |d OCLCQ | ||
| 019 | |a 269371305 |a 646768149 |a 764498301 |a 961533153 |a 962630477 |a 1086428361 | ||
| 020 | |a 9789812810106 |q (electronic bk.) | ||
| 020 | |a 9812810102 |q (electronic bk.) | ||
| 020 | |z 9789810246105 | ||
| 020 | |z 9810246102 |q (alk. paper) | ||
| 035 | |a (OCoLC)505142671 |z (OCoLC)269371305 |z (OCoLC)646768149 |z (OCoLC)764498301 |z (OCoLC)961533153 |z (OCoLC)962630477 |z (OCoLC)1086428361 | ||
| 050 | 4 | |a QA614.92 |b .Y8 2001eb | |
| 072 | 7 | |a MAT |x 038000 |2 bisacsh | |
| 082 | 7 | |a 514/.74 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Yu, Yanlin. |1 https://id.oclc.org/worldcat/entity/E39PCjKh8GfbrhhDKvQMxKPh9C |0 http://id.loc.gov/authorities/names/n2001000054 | |
| 245 | 1 | 4 | |a The index theorem and the heat equation method / |c Yanlin Yu. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (xix, 287 pages). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 490 | 1 | |a Nankai tracts in mathematics ; |v v. 2 | |
| 504 | |a Includes bibliographical references (pages 279-282) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation | |
| 505 | 8 | |a 2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR | |
| 505 | 8 | |a 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX | |
| 520 | |a This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schrödinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th. | ||
| 650 | 0 | |a Atiyah-Singer index theorem. |0 http://id.loc.gov/authorities/subjects/sh93001838 | |
| 650 | 0 | |a Heat equation. |0 http://id.loc.gov/authorities/subjects/sh85059782 | |
| 650 | 6 | |a Théorème d'Atiyah-Singer. | |
| 650 | 6 | |a Équation de la chaleur. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Atiyah-Singer index theorem |2 fast | |
| 650 | 7 | |a Heat equation |2 fast | |
| 655 | 0 | |a Electronic books. | |
| 758 | |i has work: |a The index theorem and the heat equation method (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGVJYjp3Qr9BPpVYbmKJH3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Yu, Yanlin. |t Index theorem and the heat equation method. |d Singapore ; River Edge, NJ : World Scientific, ©2001 |w (DLC) 2001017928 |
| 830 | 0 | |a Nankai tracts in mathematics ; |v v. 2. |0 http://id.loc.gov/authorities/names/n2001000055 | |
| 966 | 4 | 0 | |l DE-862 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235833 |3 Volltext |
| 966 | 4 | 0 | |l DE-863 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235833 |3 Volltext |
| 938 | |a cloudLibrary |b CLDL |n 9789812810106 | ||
| 938 | |a ebrary |b EBRY |n ebr10255391 | ||
| 938 | |a EBSCOhost |b EBSC |n 235833 | ||
| 938 | |a YBP Library Services |b YANK |n 2915206 | ||
| 936 | |a BATCHLOAD | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-862 | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn505142671 |
|---|---|
| _version_ | 1829094651394523136 |
| adam_text | |
| any_adam_object | |
| author | Yu, Yanlin |
| author_GND | http://id.loc.gov/authorities/names/n2001000054 |
| author_facet | Yu, Yanlin |
| author_role | |
| author_sort | Yu, Yanlin |
| author_variant | y y yy |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.92 .Y8 2001eb |
| callnumber-search | QA614.92 .Y8 2001eb |
| callnumber-sort | QA 3614.92 Y8 42001EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation 2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX |
| ctrlnum | (OCoLC)505142671 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05217cam a2200625 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn505142671</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20250103110447.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cn|||||||||</controlfield><controlfield tag="008">010307s2001 si ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">CaPaEBR</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">UBY</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">N$T</subfield><subfield code="d">IDEBK</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCO</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AZK</subfield><subfield code="d">LOA</subfield><subfield code="d">JBG</subfield><subfield code="d">COCUF</subfield><subfield code="d">AGLDB</subfield><subfield code="d">MOR</subfield><subfield code="d">CCO</subfield><subfield code="d">PIFAG</subfield><subfield code="d">VGM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WRM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">NRAMU</subfield><subfield code="d">VT2</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">STF</subfield><subfield code="d">M8D</subfield><subfield code="d">HS0</subfield><subfield code="d">LEAUB</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">CLOUD</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">269371305</subfield><subfield code="a">646768149</subfield><subfield code="a">764498301</subfield><subfield code="a">961533153</subfield><subfield code="a">962630477</subfield><subfield code="a">1086428361</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812810106</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812810102</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789810246105</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9810246102</subfield><subfield code="q">(alk. paper)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)505142671</subfield><subfield code="z">(OCoLC)269371305</subfield><subfield code="z">(OCoLC)646768149</subfield><subfield code="z">(OCoLC)764498301</subfield><subfield code="z">(OCoLC)961533153</subfield><subfield code="z">(OCoLC)962630477</subfield><subfield code="z">(OCoLC)1086428361</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA614.92</subfield><subfield code="b">.Y8 2001eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">038000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">514/.74</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Yu, Yanlin.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjKh8GfbrhhDKvQMxKPh9C</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2001000054</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The index theorem and the heat equation method /</subfield><subfield code="c">Yanlin Yu.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2001.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xix, 287 pages).</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Nankai tracts in mathematics ;</subfield><subfield code="v">v. 2</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 279-282) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schrödinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Atiyah-Singer index theorem.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh93001838</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Heat equation.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85059782</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorème d'Atiyah-Singer.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équation de la chaleur.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Topology.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Atiyah-Singer index theorem</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Heat equation</subfield><subfield code="2">fast</subfield></datafield><datafield tag="655" ind1=" " ind2="0"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">The index theorem and the heat equation method (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGVJYjp3Qr9BPpVYbmKJH3</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Yu, Yanlin.</subfield><subfield code="t">Index theorem and the heat equation method.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, ©2001</subfield><subfield code="w">(DLC) 2001017928</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Nankai tracts in mathematics ;</subfield><subfield code="v">v. 2.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2001000055</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-862</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235833</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-863</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235833</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">cloudLibrary</subfield><subfield code="b">CLDL</subfield><subfield code="n">9789812810106</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255391</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235833</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2915206</subfield></datafield><datafield tag="936" ind1=" " ind2=" "><subfield code="a">BATCHLOAD</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-862</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn505142671 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:36:31Z |
| institution | BVB |
| isbn | 9789812810106 9812810102 |
| language | English |
| oclc_num | 505142671 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xix, 287 pages). |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| series | Nankai tracts in mathematics ; |
| series2 | Nankai tracts in mathematics ; |
| spelling | Yu, Yanlin. https://id.oclc.org/worldcat/entity/E39PCjKh8GfbrhhDKvQMxKPh9C http://id.loc.gov/authorities/names/n2001000054 The index theorem and the heat equation method / Yanlin Yu. Singapore ; River Edge, NJ : World Scientific, ©2001. 1 online resource (xix, 287 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Nankai tracts in mathematics ; v. 2 Includes bibliographical references (pages 279-282) and index. Print version record. PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation 2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schrödinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th. Atiyah-Singer index theorem. http://id.loc.gov/authorities/subjects/sh93001838 Heat equation. http://id.loc.gov/authorities/subjects/sh85059782 Théorème d'Atiyah-Singer. Équation de la chaleur. MATHEMATICS Topology. bisacsh Atiyah-Singer index theorem fast Heat equation fast Electronic books. has work: The index theorem and the heat equation method (Text) https://id.oclc.org/worldcat/entity/E39PCGVJYjp3Qr9BPpVYbmKJH3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Yu, Yanlin. Index theorem and the heat equation method. Singapore ; River Edge, NJ : World Scientific, ©2001 (DLC) 2001017928 Nankai tracts in mathematics ; v. 2. http://id.loc.gov/authorities/names/n2001000055 |
| spellingShingle | Yu, Yanlin The index theorem and the heat equation method / Nankai tracts in mathematics ; PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation 2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX Atiyah-Singer index theorem. http://id.loc.gov/authorities/subjects/sh93001838 Heat equation. http://id.loc.gov/authorities/subjects/sh85059782 Théorème d'Atiyah-Singer. Équation de la chaleur. MATHEMATICS Topology. bisacsh Atiyah-Singer index theorem fast Heat equation fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh93001838 http://id.loc.gov/authorities/subjects/sh85059782 |
| title | The index theorem and the heat equation method / |
| title_auth | The index theorem and the heat equation method / |
| title_exact_search | The index theorem and the heat equation method / |
| title_full | The index theorem and the heat equation method / Yanlin Yu. |
| title_fullStr | The index theorem and the heat equation method / Yanlin Yu. |
| title_full_unstemmed | The index theorem and the heat equation method / Yanlin Yu. |
| title_short | The index theorem and the heat equation method / |
| title_sort | index theorem and the heat equation method |
| topic | Atiyah-Singer index theorem. http://id.loc.gov/authorities/subjects/sh93001838 Heat equation. http://id.loc.gov/authorities/subjects/sh85059782 Théorème d'Atiyah-Singer. Équation de la chaleur. MATHEMATICS Topology. bisacsh Atiyah-Singer index theorem fast Heat equation fast |
| topic_facet | Atiyah-Singer index theorem. Heat equation. Théorème d'Atiyah-Singer. Équation de la chaleur. MATHEMATICS Topology. Atiyah-Singer index theorem Heat equation Electronic books. |
| work_keys_str_mv | AT yuyanlin theindextheoremandtheheatequationmethod AT yuyanlin indextheoremandtheheatequationmethod |