Lectures on Chern-Weil theory and Witten deformations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey, N.J.
World Scientific
[2001]
|
| Series: | Nankai tracts in mathematics
Vol. 4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xi, 117 Seiten |
| ISBN: | 9810246854 9810246862 |
Staff View
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Record in the Search Index
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| adam_text | NANKAI TRACTS IN MATHEMATICS - VOL. 4 LECTURES ON CHERN-WEIL THEORY AND
WITTEN DEFORMATIONS WEIPING ZHANG NANKAI INSTITUTE OF MATHEMATICS
TIANJIN, PR CHINA WORLD SCIENTIFIC NEW JERSEY LONDON * SINGAPORE * HONG
KONG CONTENTS PREFACE VII CHAPTER 1 CHERN-WEIL THEORY FOR CHARACTERISTIC
CLASSES 1 1.1 REVIEW OF THE DE RHAM COHOMOLOGY THEORY 1 1.2 CONNECTIONS
ON VECTOR BUNDLES 3 1.3 THE CURVATURE OF A CONNECTION 4 1.4 CHERN-WEIL
THEOREM 6 1.5 CHARACTERISTIC FORMS, CLASSES AND NUMBERS 8 1.6 SOME
EXAMPLES 10 1.6.1 CHERN FORMS AND CLASSES 10 1.6.2 PONTRJAGIN CLASSES
FOR REAL VECTOR BUNDLES 11 1.6.3 HIRZEBRUCH S L-CLASS AND A-CLASS 12
1.6.4 IF-GROUPS AND THE CHERN CHARACTER 14 1.6.5 THE CHERN-SIMONS
TRANSGRESSED FORM 16 1.7 BOTT VANISHING THEOREM FOR FOLIATIONS 17 1.7.1
FOLIATIONS AND THE BOTT VANISHING THEOREM 18 1.7.2 ADIABATIC LIMIT AND
THE BOTT CONNECTION 20 1.8 CHERN-WEIL THEORY IN ODD DIMENSION 22 1.9
REFERENCES 26 CHAPTER 2 BOTT AND DUISTERMAAT-HECKMAN FORMULAS 29 2.1
BERLINE-VERGNE LOCALIZATION FORMULA 29 2.2 BOTT RESIDUE FORMULA 35 2.3
DUISTERMAAT-HECKMAN FORMULA 37 2.4 BOTT S ORIGINAL IDEA 38 IX X CONTENTS
2.5 REFERENCES 39 CHAPTER 3 GAUSS-BONNET-CHERN THEOREM 41 3.1 A TOY
MODEL AND THE BEREZIN INTEGRAL 41 3 .2 MATHAI-QUILLEN S THORN FORM 43
3.3 A TRANSGRESSION FORMULA 46 3.4 PROOF OF THE GAUSS-BONNET-CHERN
THEOREM 47 3.5 SOME REMARKS 50 3.6 CHERN S ORIGINAL PROOF 51 3.7
REFERENCES 54 CHAPTER 4 POINCARE-HOPF INDEX FORMULA: AN ANALYTIC PROOF
57 4.1 REVIEW OF HODGE THEOREM 57 4.2 POINCARE-HOPF INDEX FORMULA 60 4.3
CLIFFORD ACTIONS AND THE WITTEN DEFORMATION 61 4.4 AN ESTIMATE OUTSIDE
OF UPGJ5 ERO (V)[/P 63 4.5 HARMONIC OSCILLATORS ON EUCLIDEAN SPACES 64
4.6 A PROOF OF THE POINCARE-HOPF INDEX FORMULA 67 4.7 SOME ESTIMATES FOR
D T /S, 2 I 4 69 4.8 AN ALTERNATE ANALYTIC PROOF 73 4.9 REFERENCES
74 CHAPTER 5 MORSE INEQUALITIES: AN ANALYTIC PROOF 75 5.1 REVIEW OF
MORSE INEQUALITIES 75 5.2 WITTEN DEFORMATION 77 5.3 HODGE THEOREM FOR
(SL*(M),D T F) 78 5.4 BEHAVIOUR OF OJ NEAR THE CRITICAL POINTS OF / 79
5.5 PROOF OF MORSE INEQUALITIES 81 5.6 PROOF OF PROPOSITION 5.5 83 5.7
SOME REMARKS AND COMMENTS 88 5.8 REFERENCES 89 CHAPTER 6 THOM-SMALE AND
WITTEN COMPLEXES 93 6.1 THE THOM-SMALE COMPLEX 93 6.2 THE DE RHAM MAP
FOR THOM-SMALE COMPLEXES 95 6.3 WITTEN S INSTANTON COMPLEX AND THE MAP
ER 97 6.4 THE MAP P^RER 100 6.5 AN ANALYTIC PROOF OF THEOREM 6.4 102
CONTENTS XI 6.6 REFERENCES 102 CHAPTER 7 ATIYAH THEOREM ON KERVAIRE
SEMI-CHARACTERISTIC 105 7.1 KERVAIRE SEMI-CHARACTERISTIC 106 7.2
ATIYAH S ORIGINAL PROOF 107 7.3 A PROOF VIA WITTEN DEFORMATION 108 7.4 A
GENERIC COUNTING FORMULA FOR K(M) 112 7.5 NON-MULTIPLICATIVITY OF K(M)
113 7.6 REFERENCES 115 INDEX 117
|
| any_adam_object | 1 |
| author | Zhang, Weiping |
| author_GND | (DE-588)105577016X |
| author_facet | Zhang, Weiping |
| author_role | aut |
| author_sort | Zhang, Weiping |
| author_variant | w z wz |
| building | Verbundindex |
| bvnumber | BV014137942 |
| classification_rvk | SK 350 SK 370 |
| ctrlnum | (OCoLC)247954818 (DE-599)BVBBV014137942 |
| dewey-full | 514.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.72 |
| dewey-search | 514.72 |
| dewey-sort | 3514.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014137942 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:58:19Z |
| institution | BVB |
| isbn | 9810246854 9810246862 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009687608 |
| oclc_num | 247954818 |
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| physical | xi, 117 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific |
| record_format | marc |
| series | Nankai tracts in mathematics |
| series2 | Nankai tracts in mathematics |
| spelling | Zhang, Weiping Verfasser (DE-588)105577016X aut Lectures on Chern-Weil theory and Witten deformations Weiping Zhang (Nankai Institute of Mathematics Tianjin, P R China) New Jersey, N.J. World Scientific [2001] © 2001 xi, 117 Seiten txt rdacontent n rdamedia nc rdacarrier Nankai tracts in mathematics Vol. 4 Includes bibliographical references and index Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Poincaré-Indexmethode (DE-588)4174969-8 gnd rswk-swf Chern-Klasse (DE-588)4306750-5 gnd rswk-swf Chern-Klasse (DE-588)4306750-5 s DE-604 Poincaré-Indexmethode (DE-588)4174969-8 s Morse-Theorie (DE-588)4197103-6 s Nankai tracts in mathematics Vol. 4 (DE-604)BV014017593 4 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009687608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Weiping Lectures on Chern-Weil theory and Witten deformations Nankai tracts in mathematics Morse-Theorie (DE-588)4197103-6 gnd Poincaré-Indexmethode (DE-588)4174969-8 gnd Chern-Klasse (DE-588)4306750-5 gnd |
| subject_GND | (DE-588)4197103-6 (DE-588)4174969-8 (DE-588)4306750-5 |
| title | Lectures on Chern-Weil theory and Witten deformations |
| title_auth | Lectures on Chern-Weil theory and Witten deformations |
| title_exact_search | Lectures on Chern-Weil theory and Witten deformations |
| title_full | Lectures on Chern-Weil theory and Witten deformations Weiping Zhang (Nankai Institute of Mathematics Tianjin, P R China) |
| title_fullStr | Lectures on Chern-Weil theory and Witten deformations Weiping Zhang (Nankai Institute of Mathematics Tianjin, P R China) |
| title_full_unstemmed | Lectures on Chern-Weil theory and Witten deformations Weiping Zhang (Nankai Institute of Mathematics Tianjin, P R China) |
| title_short | Lectures on Chern-Weil theory and Witten deformations |
| title_sort | lectures on chern weil theory and witten deformations |
| topic | Morse-Theorie (DE-588)4197103-6 gnd Poincaré-Indexmethode (DE-588)4174969-8 gnd Chern-Klasse (DE-588)4306750-5 gnd |
| topic_facet | Morse-Theorie Poincaré-Indexmethode Chern-Klasse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009687608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT zhangweiping lecturesonchernweiltheoryandwittendeformations |