Algebraic topology via differential geometry /:
In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduce...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English French |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1987.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
99. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry. |
| Beschreibung: | Translation of: Méthodes de géométrie différentielle en topologie algébrique. |
| Beschreibung: | 1 online resource (363 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (page 360) and index. |
| ISBN: | 9781107361317 1107361311 0511629370 9780511629372 1139884220 9781139884228 1107366224 9781107366220 1107370957 9781107370951 1107369967 9781107369962 1299404022 9781299404021 1107363764 9781107363762 |
| ISSN: | 0076-0552 ; |
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| 240 | 1 | 0 | |a Méthodes de géométrie différentielle en topologie algébrique. |l English |
| 245 | 1 | 0 | |a Algebraic topology via differential geometry / |c M. Karoubi and C. Leruste. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York : |b Cambridge University Press, |c 1987. | ||
| 300 | |a 1 online resource (363 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series, |x 0076-0552 ; |v 99 | |
| 500 | |a Translation of: Méthodes de géométrie différentielle en topologie algébrique. | ||
| 504 | |a Includes bibliographical references (page 360) and index. | ||
| 546 | |a Translation of: Methodes de geometrie differentielle en topologie algebrique. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Introduction; I ALGEBRAIC PRELIMINARIES; 1 BILINEAR MAPS; 2 TENSOR PRODUCT OF TWO VECTOR SPACES; 2.1 Theorem: This construction can always be performed.; 2.2 Remarks:; 2. 3 Proposition; 2.4 Notation; 2.5 Theorem; 2.6 Corollary:; 2.7 Tensor product of Abelian groups; 3 COMMUTATIVITY. ASSOCIATIVITY; 3.1 Theorem:; 3.2 Theorem:; 3.3 Theorem:; 3.4 Remark:; 4 TENSOR PRODUCT OF LINEAR MAPS; 4.1 Theorem:; 4.2 Remark:; 4. 3 Proposi tion:; 5 TENSOR PRODUCT WITH A DIRECT SUM ('DISTRIBUTIVITY'); 5.1 Theorem; 5.2 Corollary; 5.3 Corollary; 6 EXACT SEQUENCES | |
| 505 | 8 | |a 6.1 Definitions:6.2 Remark:; 6.3 Examples:; 6.4 Definition:; 6.5 Lemma:; 6.6 Corollary:; 6.7 Theorem:; 6.8 Important Remark:; 6.9 Theorem:; 6.10 Corollary.; 6.11 Remark:; 7 TENSOR ALGEBRA; 7.1 Definitions:; 7.2 Theorem:; 7.3 Remark:; 7.4 Theorem:; 7.5 Remark:; 7.6 Theorem:; 8 EXTERIOR POWERS. EXTERIOR ALGEBRA; 8.1 Definition:; 8.2 Proposition:; 8.3 Definitions:; 8.4 Remark:; 8.5 Theorem:; 8.6 Definition:; 8.7 Theorem:; 8.8 Remark:; 8.9 Theorem:; 8.10 Theorem:; 8.11 Theorem:; 8.12 Theorem:; 9 SYMMETRIC POWERS. SYMMETRIC ALGEBRA; 9.1 Definition:; 9.2 Definition:; 9.3 Theorem:; 9.4 Definition | |
| 505 | 8 | |a 9.5 Theorem:9.6 Theorem:; 9.7 Theorem:; 10 DUALITY; 10.1 Theorem:; 10.2 Corollary:; 10.3 Theorem; 11 MODULES; II DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rn; 0 ELEMENTARY RESULTS OF DIFFERENTIAL CALCULUS; 0.1 First Order; 0.2 Second and Higher Orders; 1 DIFFERENTIAL FORMS; 1.1 -Definition:; 1.2 Definition:; 1.3 Remarks:; 1.4 Theorem:; 1.5 Remark:; 1.6 Notation:; 1.7 Example:; 2 EXTERIOR DIFFERENTIAL; 2.1 Theorem:; 2.2 Example:; 2 . 3 Theorem:; 2.4 Example:; 2.5 Theorem:; 3 INVERSE IMAGE OF A DIFFERENTIAL FORM; 3.1 Theorem:; 3.2 Explicit Formula; 4 DB i?HAM COHOMOLOGY; 4.1 Definition | |
| 505 | 8 | |a 4.2 Remark:4.3 Remark:; 4.4 Theorem:; 5 HOMOTOPY; 5.1 Definition:; 5.2 Structure of (UxR; 5.3 Lemma:; 5.4 Definition:; 5.5 Lemma:; 5.6 Definition:; 5.7 Definition:; 5.8 Theorem:; 5.9 Corollary:; 6 COHOMOLOGY OF Rn; 6 .1 Lemma; 6.2 Lemma:; 6.3 Theorem:; 6.4 Remark:; 7 COHCMOLOGY OF R2\{0}; 7.1 Lemma:; 7.2 Theorem:; 7.3 Technical Lemma:; 7.4 Theorem:; 7.5 Corollary:; 7.6 Theorem:; 7.7 Corollary:; 7.8 Recapitulation:; 8 DIFFERENTIAL FORMS WITH COMPACT SUPPORTS; 8.1 Lemma:; 8.2 Definitions:; 8.3 Important Remark:; 8.4 Theorem:; 8.5 Theorem:; 8.6 Theorem:; 8.7 Remarks | |
| 505 | 8 | |a III DIFFERENTIABLE MANIFOLDS1 TOPOLOGICAL MANIFOLDS; 1.1 Definition:; 1.2 Remarks; 1.3 Theorem:; 1.4 Theorem:; 1.5 Theorem:; 1.6 Definition:; 2 FIRST EXAMPLES; 2.1 Example:; 2.2 Example:; 2.3 Remark:; 2.4 Definitions:; 2.5 Lemma:; 2.6 Lenma:; 2.7 Theorem:; 2.8 Theorem:; 2.9 Theorem:; 2.10 Theorem:; 3 THE IMPLICIT FUNCTION THEOREM; 3.1 Theorem; 3.2 Corollary.; 3.3 Remark:; 4 EXAMPLES RESUMED; 4.1 Example:; 4.2 Definition:; 4.3 Theorem:; 4.4 Corollary:; 4.5 Remark:; 4.6 Theorem:; 4.7 Definition:; 4.8 Theorem:; 4.10 Theorem:; 4.11 Important Remark:; 4.12 Lemma:; 4.13 Corollary:; 4.14 Theorem | |
| 650 | 0 | |a Algebraic topology. |0 http://id.loc.gov/authorities/subjects/sh85003438 | |
| 650 | 0 | |a Geometry, Differential. |0 http://id.loc.gov/authorities/subjects/sh85054146 | |
| 650 | 6 | |a Topologie algébrique. | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Algebraic topology |2 fast | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Algebraische Topologie |2 gnd |0 http://d-nb.info/gnd/4120861-4 | |
| 650 | 7 | |a DeRham-Kohomologie |2 gnd |0 http://d-nb.info/gnd/4352640-8 | |
| 650 | 7 | |a Geometrie |2 gnd |0 http://d-nb.info/gnd/4020236-7 | |
| 650 | 7 | |a Mannigfaltigkeit |2 gnd |0 http://d-nb.info/gnd/4037379-4 | |
| 650 | 7 | |a Topologische Algebra |2 gnd |0 http://d-nb.info/gnd/4377377-1 | |
| 650 | 7 | |a Differenzierbare Mannigfaltigkeit |2 gnd |0 http://d-nb.info/gnd/4012269-4 | |
| 650 | 7 | |a Geometria diferencial (textos avançados) |2 larpcal | |
| 650 | 7 | |a Topologia algébrica. |2 larpcal | |
| 650 | 7 | |a Cohomologia. |2 larpcal | |
| 650 | 7 | |a Topologie algébrique. |2 ram | |
| 650 | 7 | |a Géométrie différentielle. |2 ram | |
| 700 | 1 | |a Leruste, C. | |
| 776 | 0 | 8 | |i Print version: |a Karoubi, Max. |s Méthodes de géométrie différentielle en topologie algébrique. English. |t Algebraic topology via differential geometry. |d Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987 |z 0521317142 |w (DLC) 86017087 |w (OCoLC)13823350 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 99. |x 0076-0552 |0 http://id.loc.gov/authorities/names/n42015587 | |
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| contents | Cover; Title; Copyright; Contents; Introduction; I ALGEBRAIC PRELIMINARIES; 1 BILINEAR MAPS; 2 TENSOR PRODUCT OF TWO VECTOR SPACES; 2.1 Theorem: This construction can always be performed.; 2.2 Remarks:; 2. 3 Proposition; 2.4 Notation; 2.5 Theorem; 2.6 Corollary:; 2.7 Tensor product of Abelian groups; 3 COMMUTATIVITY. ASSOCIATIVITY; 3.1 Theorem:; 3.2 Theorem:; 3.3 Theorem:; 3.4 Remark:; 4 TENSOR PRODUCT OF LINEAR MAPS; 4.1 Theorem:; 4.2 Remark:; 4. 3 Proposi tion:; 5 TENSOR PRODUCT WITH A DIRECT SUM ('DISTRIBUTIVITY'); 5.1 Theorem; 5.2 Corollary; 5.3 Corollary; 6 EXACT SEQUENCES 6.1 Definitions:6.2 Remark:; 6.3 Examples:; 6.4 Definition:; 6.5 Lemma:; 6.6 Corollary:; 6.7 Theorem:; 6.8 Important Remark:; 6.9 Theorem:; 6.10 Corollary.; 6.11 Remark:; 7 TENSOR ALGEBRA; 7.1 Definitions:; 7.2 Theorem:; 7.3 Remark:; 7.4 Theorem:; 7.5 Remark:; 7.6 Theorem:; 8 EXTERIOR POWERS. EXTERIOR ALGEBRA; 8.1 Definition:; 8.2 Proposition:; 8.3 Definitions:; 8.4 Remark:; 8.5 Theorem:; 8.6 Definition:; 8.7 Theorem:; 8.8 Remark:; 8.9 Theorem:; 8.10 Theorem:; 8.11 Theorem:; 8.12 Theorem:; 9 SYMMETRIC POWERS. SYMMETRIC ALGEBRA; 9.1 Definition:; 9.2 Definition:; 9.3 Theorem:; 9.4 Definition 9.5 Theorem:9.6 Theorem:; 9.7 Theorem:; 10 DUALITY; 10.1 Theorem:; 10.2 Corollary:; 10.3 Theorem; 11 MODULES; II DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rn; 0 ELEMENTARY RESULTS OF DIFFERENTIAL CALCULUS; 0.1 First Order; 0.2 Second and Higher Orders; 1 DIFFERENTIAL FORMS; 1.1 -Definition:; 1.2 Definition:; 1.3 Remarks:; 1.4 Theorem:; 1.5 Remark:; 1.6 Notation:; 1.7 Example:; 2 EXTERIOR DIFFERENTIAL; 2.1 Theorem:; 2.2 Example:; 2 . 3 Theorem:; 2.4 Example:; 2.5 Theorem:; 3 INVERSE IMAGE OF A DIFFERENTIAL FORM; 3.1 Theorem:; 3.2 Explicit Formula; 4 DB i?HAM COHOMOLOGY; 4.1 Definition 4.2 Remark:4.3 Remark:; 4.4 Theorem:; 5 HOMOTOPY; 5.1 Definition:; 5.2 Structure of (UxR; 5.3 Lemma:; 5.4 Definition:; 5.5 Lemma:; 5.6 Definition:; 5.7 Definition:; 5.8 Theorem:; 5.9 Corollary:; 6 COHOMOLOGY OF Rn; 6 .1 Lemma; 6.2 Lemma:; 6.3 Theorem:; 6.4 Remark:; 7 COHCMOLOGY OF R2\{0}; 7.1 Lemma:; 7.2 Theorem:; 7.3 Technical Lemma:; 7.4 Theorem:; 7.5 Corollary:; 7.6 Theorem:; 7.7 Corollary:; 7.8 Recapitulation:; 8 DIFFERENTIAL FORMS WITH COMPACT SUPPORTS; 8.1 Lemma:; 8.2 Definitions:; 8.3 Important Remark:; 8.4 Theorem:; 8.5 Theorem:; 8.6 Theorem:; 8.7 Remarks III DIFFERENTIABLE MANIFOLDS1 TOPOLOGICAL MANIFOLDS; 1.1 Definition:; 1.2 Remarks; 1.3 Theorem:; 1.4 Theorem:; 1.5 Theorem:; 1.6 Definition:; 2 FIRST EXAMPLES; 2.1 Example:; 2.2 Example:; 2.3 Remark:; 2.4 Definitions:; 2.5 Lemma:; 2.6 Lenma:; 2.7 Theorem:; 2.8 Theorem:; 2.9 Theorem:; 2.10 Theorem:; 3 THE IMPLICIT FUNCTION THEOREM; 3.1 Theorem; 3.2 Corollary.; 3.3 Remark:; 4 EXAMPLES RESUMED; 4.1 Example:; 4.2 Definition:; 4.3 Theorem:; 4.4 Corollary:; 4.5 Remark:; 4.6 Theorem:; 4.7 Definition:; 4.8 Theorem:; 4.10 Theorem:; 4.11 Important Remark:; 4.12 Lemma:; 4.13 Corollary:; 4.14 Theorem |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Title; Copyright; Contents; Introduction; I ALGEBRAIC PRELIMINARIES; 1 BILINEAR MAPS; 2 TENSOR PRODUCT OF TWO VECTOR SPACES; 2.1 Theorem: This construction can always be performed.; 2.2 Remarks:; 2. 3 Proposition; 2.4 Notation; 2.5 Theorem; 2.6 Corollary:; 2.7 Tensor product of Abelian groups; 3 COMMUTATIVITY. ASSOCIATIVITY; 3.1 Theorem:; 3.2 Theorem:; 3.3 Theorem:; 3.4 Remark:; 4 TENSOR PRODUCT OF LINEAR MAPS; 4.1 Theorem:; 4.2 Remark:; 4. 3 Proposi tion:; 5 TENSOR PRODUCT WITH A DIRECT SUM ('DISTRIBUTIVITY'); 5.1 Theorem; 5.2 Corollary; 5.3 Corollary; 6 EXACT SEQUENCES</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.1 Definitions:6.2 Remark:; 6.3 Examples:; 6.4 Definition:; 6.5 Lemma:; 6.6 Corollary:; 6.7 Theorem:; 6.8 Important Remark:; 6.9 Theorem:; 6.10 Corollary.; 6.11 Remark:; 7 TENSOR ALGEBRA; 7.1 Definitions:; 7.2 Theorem:; 7.3 Remark:; 7.4 Theorem:; 7.5 Remark:; 7.6 Theorem:; 8 EXTERIOR POWERS. EXTERIOR ALGEBRA; 8.1 Definition:; 8.2 Proposition:; 8.3 Definitions:; 8.4 Remark:; 8.5 Theorem:; 8.6 Definition:; 8.7 Theorem:; 8.8 Remark:; 8.9 Theorem:; 8.10 Theorem:; 8.11 Theorem:; 8.12 Theorem:; 9 SYMMETRIC POWERS. SYMMETRIC ALGEBRA; 9.1 Definition:; 9.2 Definition:; 9.3 Theorem:; 9.4 Definition</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">9.5 Theorem:9.6 Theorem:; 9.7 Theorem:; 10 DUALITY; 10.1 Theorem:; 10.2 Corollary:; 10.3 Theorem; 11 MODULES; II DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rn; 0 ELEMENTARY RESULTS OF DIFFERENTIAL CALCULUS; 0.1 First Order; 0.2 Second and Higher Orders; 1 DIFFERENTIAL FORMS; 1.1 -Definition:; 1.2 Definition:; 1.3 Remarks:; 1.4 Theorem:; 1.5 Remark:; 1.6 Notation:; 1.7 Example:; 2 EXTERIOR DIFFERENTIAL; 2.1 Theorem:; 2.2 Example:; 2 . 3 Theorem:; 2.4 Example:; 2.5 Theorem:; 3 INVERSE IMAGE OF A DIFFERENTIAL FORM; 3.1 Theorem:; 3.2 Explicit Formula; 4 DB i?HAM COHOMOLOGY; 4.1 Definition</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.2 Remark:4.3 Remark:; 4.4 Theorem:; 5 HOMOTOPY; 5.1 Definition:; 5.2 Structure of (UxR; 5.3 Lemma:; 5.4 Definition:; 5.5 Lemma:; 5.6 Definition:; 5.7 Definition:; 5.8 Theorem:; 5.9 Corollary:; 6 COHOMOLOGY OF Rn; 6 .1 Lemma; 6.2 Lemma:; 6.3 Theorem:; 6.4 Remark:; 7 COHCMOLOGY OF R2\{0}; 7.1 Lemma:; 7.2 Theorem:; 7.3 Technical Lemma:; 7.4 Theorem:; 7.5 Corollary:; 7.6 Theorem:; 7.7 Corollary:; 7.8 Recapitulation:; 8 DIFFERENTIAL FORMS WITH COMPACT SUPPORTS; 8.1 Lemma:; 8.2 Definitions:; 8.3 Important Remark:; 8.4 Theorem:; 8.5 Theorem:; 8.6 Theorem:; 8.7 Remarks</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">III DIFFERENTIABLE MANIFOLDS1 TOPOLOGICAL MANIFOLDS; 1.1 Definition:; 1.2 Remarks; 1.3 Theorem:; 1.4 Theorem:; 1.5 Theorem:; 1.6 Definition:; 2 FIRST EXAMPLES; 2.1 Example:; 2.2 Example:; 2.3 Remark:; 2.4 Definitions:; 2.5 Lemma:; 2.6 Lenma:; 2.7 Theorem:; 2.8 Theorem:; 2.9 Theorem:; 2.10 Theorem:; 3 THE IMPLICIT FUNCTION THEOREM; 3.1 Theorem; 3.2 Corollary.; 3.3 Remark:; 4 EXAMPLES RESUMED; 4.1 Example:; 4.2 Definition:; 4.3 Theorem:; 4.4 Corollary:; 4.5 Remark:; 4.6 Theorem:; 4.7 Definition:; 4.8 Theorem:; 4.10 Theorem:; 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| id | ZDB-4-EBA-ocn840416224 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:18Z |
| institution | BVB |
| isbn | 9781107361317 1107361311 0511629370 9780511629372 1139884220 9781139884228 1107366224 9781107366220 1107370957 9781107370951 1107369967 9781107369962 1299404022 9781299404021 1107363764 9781107363762 |
| issn | 0076-0552 ; |
| language | English French |
| oclc_num | 840416224 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (363 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series, |
| spelling | Karoubi, Max. Méthodes de géométrie différentielle en topologie algébrique. English Algebraic topology via differential geometry / M. Karoubi and C. Leruste. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987. 1 online resource (363 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series, 0076-0552 ; 99 Translation of: Méthodes de géométrie différentielle en topologie algébrique. Includes bibliographical references (page 360) and index. Translation of: Methodes de geometrie differentielle en topologie algebrique. Print version record. In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry. Cover; Title; Copyright; Contents; Introduction; I ALGEBRAIC PRELIMINARIES; 1 BILINEAR MAPS; 2 TENSOR PRODUCT OF TWO VECTOR SPACES; 2.1 Theorem: This construction can always be performed.; 2.2 Remarks:; 2. 3 Proposition; 2.4 Notation; 2.5 Theorem; 2.6 Corollary:; 2.7 Tensor product of Abelian groups; 3 COMMUTATIVITY. ASSOCIATIVITY; 3.1 Theorem:; 3.2 Theorem:; 3.3 Theorem:; 3.4 Remark:; 4 TENSOR PRODUCT OF LINEAR MAPS; 4.1 Theorem:; 4.2 Remark:; 4. 3 Proposi tion:; 5 TENSOR PRODUCT WITH A DIRECT SUM ('DISTRIBUTIVITY'); 5.1 Theorem; 5.2 Corollary; 5.3 Corollary; 6 EXACT SEQUENCES 6.1 Definitions:6.2 Remark:; 6.3 Examples:; 6.4 Definition:; 6.5 Lemma:; 6.6 Corollary:; 6.7 Theorem:; 6.8 Important Remark:; 6.9 Theorem:; 6.10 Corollary.; 6.11 Remark:; 7 TENSOR ALGEBRA; 7.1 Definitions:; 7.2 Theorem:; 7.3 Remark:; 7.4 Theorem:; 7.5 Remark:; 7.6 Theorem:; 8 EXTERIOR POWERS. EXTERIOR ALGEBRA; 8.1 Definition:; 8.2 Proposition:; 8.3 Definitions:; 8.4 Remark:; 8.5 Theorem:; 8.6 Definition:; 8.7 Theorem:; 8.8 Remark:; 8.9 Theorem:; 8.10 Theorem:; 8.11 Theorem:; 8.12 Theorem:; 9 SYMMETRIC POWERS. SYMMETRIC ALGEBRA; 9.1 Definition:; 9.2 Definition:; 9.3 Theorem:; 9.4 Definition 9.5 Theorem:9.6 Theorem:; 9.7 Theorem:; 10 DUALITY; 10.1 Theorem:; 10.2 Corollary:; 10.3 Theorem; 11 MODULES; II DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rn; 0 ELEMENTARY RESULTS OF DIFFERENTIAL CALCULUS; 0.1 First Order; 0.2 Second and Higher Orders; 1 DIFFERENTIAL FORMS; 1.1 -Definition:; 1.2 Definition:; 1.3 Remarks:; 1.4 Theorem:; 1.5 Remark:; 1.6 Notation:; 1.7 Example:; 2 EXTERIOR DIFFERENTIAL; 2.1 Theorem:; 2.2 Example:; 2 . 3 Theorem:; 2.4 Example:; 2.5 Theorem:; 3 INVERSE IMAGE OF A DIFFERENTIAL FORM; 3.1 Theorem:; 3.2 Explicit Formula; 4 DB i?HAM COHOMOLOGY; 4.1 Definition 4.2 Remark:4.3 Remark:; 4.4 Theorem:; 5 HOMOTOPY; 5.1 Definition:; 5.2 Structure of (UxR; 5.3 Lemma:; 5.4 Definition:; 5.5 Lemma:; 5.6 Definition:; 5.7 Definition:; 5.8 Theorem:; 5.9 Corollary:; 6 COHOMOLOGY OF Rn; 6 .1 Lemma; 6.2 Lemma:; 6.3 Theorem:; 6.4 Remark:; 7 COHCMOLOGY OF R2\{0}; 7.1 Lemma:; 7.2 Theorem:; 7.3 Technical Lemma:; 7.4 Theorem:; 7.5 Corollary:; 7.6 Theorem:; 7.7 Corollary:; 7.8 Recapitulation:; 8 DIFFERENTIAL FORMS WITH COMPACT SUPPORTS; 8.1 Lemma:; 8.2 Definitions:; 8.3 Important Remark:; 8.4 Theorem:; 8.5 Theorem:; 8.6 Theorem:; 8.7 Remarks III DIFFERENTIABLE MANIFOLDS1 TOPOLOGICAL MANIFOLDS; 1.1 Definition:; 1.2 Remarks; 1.3 Theorem:; 1.4 Theorem:; 1.5 Theorem:; 1.6 Definition:; 2 FIRST EXAMPLES; 2.1 Example:; 2.2 Example:; 2.3 Remark:; 2.4 Definitions:; 2.5 Lemma:; 2.6 Lenma:; 2.7 Theorem:; 2.8 Theorem:; 2.9 Theorem:; 2.10 Theorem:; 3 THE IMPLICIT FUNCTION THEOREM; 3.1 Theorem; 3.2 Corollary.; 3.3 Remark:; 4 EXAMPLES RESUMED; 4.1 Example:; 4.2 Definition:; 4.3 Theorem:; 4.4 Corollary:; 4.5 Remark:; 4.6 Theorem:; 4.7 Definition:; 4.8 Theorem:; 4.10 Theorem:; 4.11 Important Remark:; 4.12 Lemma:; 4.13 Corollary:; 4.14 Theorem Algebraic topology. http://id.loc.gov/authorities/subjects/sh85003438 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Topologie algébrique. Géométrie différentielle. MATHEMATICS Algebra Linear. bisacsh Algebraic topology fast Geometry, Differential fast Algebraische Topologie gnd http://d-nb.info/gnd/4120861-4 DeRham-Kohomologie gnd http://d-nb.info/gnd/4352640-8 Geometrie gnd http://d-nb.info/gnd/4020236-7 Mannigfaltigkeit gnd http://d-nb.info/gnd/4037379-4 Topologische Algebra gnd http://d-nb.info/gnd/4377377-1 Differenzierbare Mannigfaltigkeit gnd http://d-nb.info/gnd/4012269-4 Geometria diferencial (textos avançados) larpcal Topologia algébrica. larpcal Cohomologia. larpcal Topologie algébrique. ram Géométrie différentielle. ram Leruste, C. Print version: Karoubi, Max. Méthodes de géométrie différentielle en topologie algébrique. English. Algebraic topology via differential geometry. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987 0521317142 (DLC) 86017087 (OCoLC)13823350 London Mathematical Society lecture note series ; 99. 0076-0552 http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552511 Volltext |
| spellingShingle | Karoubi, Max Algebraic topology via differential geometry / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Introduction; I ALGEBRAIC PRELIMINARIES; 1 BILINEAR MAPS; 2 TENSOR PRODUCT OF TWO VECTOR SPACES; 2.1 Theorem: This construction can always be performed.; 2.2 Remarks:; 2. 3 Proposition; 2.4 Notation; 2.5 Theorem; 2.6 Corollary:; 2.7 Tensor product of Abelian groups; 3 COMMUTATIVITY. ASSOCIATIVITY; 3.1 Theorem:; 3.2 Theorem:; 3.3 Theorem:; 3.4 Remark:; 4 TENSOR PRODUCT OF LINEAR MAPS; 4.1 Theorem:; 4.2 Remark:; 4. 3 Proposi tion:; 5 TENSOR PRODUCT WITH A DIRECT SUM ('DISTRIBUTIVITY'); 5.1 Theorem; 5.2 Corollary; 5.3 Corollary; 6 EXACT SEQUENCES 6.1 Definitions:6.2 Remark:; 6.3 Examples:; 6.4 Definition:; 6.5 Lemma:; 6.6 Corollary:; 6.7 Theorem:; 6.8 Important Remark:; 6.9 Theorem:; 6.10 Corollary.; 6.11 Remark:; 7 TENSOR ALGEBRA; 7.1 Definitions:; 7.2 Theorem:; 7.3 Remark:; 7.4 Theorem:; 7.5 Remark:; 7.6 Theorem:; 8 EXTERIOR POWERS. EXTERIOR ALGEBRA; 8.1 Definition:; 8.2 Proposition:; 8.3 Definitions:; 8.4 Remark:; 8.5 Theorem:; 8.6 Definition:; 8.7 Theorem:; 8.8 Remark:; 8.9 Theorem:; 8.10 Theorem:; 8.11 Theorem:; 8.12 Theorem:; 9 SYMMETRIC POWERS. SYMMETRIC ALGEBRA; 9.1 Definition:; 9.2 Definition:; 9.3 Theorem:; 9.4 Definition 9.5 Theorem:9.6 Theorem:; 9.7 Theorem:; 10 DUALITY; 10.1 Theorem:; 10.2 Corollary:; 10.3 Theorem; 11 MODULES; II DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rn; 0 ELEMENTARY RESULTS OF DIFFERENTIAL CALCULUS; 0.1 First Order; 0.2 Second and Higher Orders; 1 DIFFERENTIAL FORMS; 1.1 -Definition:; 1.2 Definition:; 1.3 Remarks:; 1.4 Theorem:; 1.5 Remark:; 1.6 Notation:; 1.7 Example:; 2 EXTERIOR DIFFERENTIAL; 2.1 Theorem:; 2.2 Example:; 2 . 3 Theorem:; 2.4 Example:; 2.5 Theorem:; 3 INVERSE IMAGE OF A DIFFERENTIAL FORM; 3.1 Theorem:; 3.2 Explicit Formula; 4 DB i?HAM COHOMOLOGY; 4.1 Definition 4.2 Remark:4.3 Remark:; 4.4 Theorem:; 5 HOMOTOPY; 5.1 Definition:; 5.2 Structure of (UxR; 5.3 Lemma:; 5.4 Definition:; 5.5 Lemma:; 5.6 Definition:; 5.7 Definition:; 5.8 Theorem:; 5.9 Corollary:; 6 COHOMOLOGY OF Rn; 6 .1 Lemma; 6.2 Lemma:; 6.3 Theorem:; 6.4 Remark:; 7 COHCMOLOGY OF R2\{0}; 7.1 Lemma:; 7.2 Theorem:; 7.3 Technical Lemma:; 7.4 Theorem:; 7.5 Corollary:; 7.6 Theorem:; 7.7 Corollary:; 7.8 Recapitulation:; 8 DIFFERENTIAL FORMS WITH COMPACT SUPPORTS; 8.1 Lemma:; 8.2 Definitions:; 8.3 Important Remark:; 8.4 Theorem:; 8.5 Theorem:; 8.6 Theorem:; 8.7 Remarks III DIFFERENTIABLE MANIFOLDS1 TOPOLOGICAL MANIFOLDS; 1.1 Definition:; 1.2 Remarks; 1.3 Theorem:; 1.4 Theorem:; 1.5 Theorem:; 1.6 Definition:; 2 FIRST EXAMPLES; 2.1 Example:; 2.2 Example:; 2.3 Remark:; 2.4 Definitions:; 2.5 Lemma:; 2.6 Lenma:; 2.7 Theorem:; 2.8 Theorem:; 2.9 Theorem:; 2.10 Theorem:; 3 THE IMPLICIT FUNCTION THEOREM; 3.1 Theorem; 3.2 Corollary.; 3.3 Remark:; 4 EXAMPLES RESUMED; 4.1 Example:; 4.2 Definition:; 4.3 Theorem:; 4.4 Corollary:; 4.5 Remark:; 4.6 Theorem:; 4.7 Definition:; 4.8 Theorem:; 4.10 Theorem:; 4.11 Important Remark:; 4.12 Lemma:; 4.13 Corollary:; 4.14 Theorem Algebraic topology. http://id.loc.gov/authorities/subjects/sh85003438 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Topologie algébrique. Géométrie différentielle. MATHEMATICS Algebra Linear. bisacsh Algebraic topology fast Geometry, Differential fast Algebraische Topologie gnd http://d-nb.info/gnd/4120861-4 DeRham-Kohomologie gnd http://d-nb.info/gnd/4352640-8 Geometrie gnd http://d-nb.info/gnd/4020236-7 Mannigfaltigkeit gnd http://d-nb.info/gnd/4037379-4 Topologische Algebra gnd http://d-nb.info/gnd/4377377-1 Differenzierbare Mannigfaltigkeit gnd http://d-nb.info/gnd/4012269-4 Geometria diferencial (textos avançados) larpcal Topologia algébrica. larpcal Cohomologia. larpcal Topologie algébrique. ram Géométrie différentielle. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003438 http://id.loc.gov/authorities/subjects/sh85054146 http://d-nb.info/gnd/4120861-4 http://d-nb.info/gnd/4352640-8 http://d-nb.info/gnd/4020236-7 http://d-nb.info/gnd/4037379-4 http://d-nb.info/gnd/4377377-1 http://d-nb.info/gnd/4012269-4 |
| title | Algebraic topology via differential geometry / |
| title_alt | Méthodes de géométrie différentielle en topologie algébrique. |
| title_auth | Algebraic topology via differential geometry / |
| title_exact_search | Algebraic topology via differential geometry / |
| title_full | Algebraic topology via differential geometry / M. Karoubi and C. Leruste. |
| title_fullStr | Algebraic topology via differential geometry / M. Karoubi and C. Leruste. |
| title_full_unstemmed | Algebraic topology via differential geometry / M. Karoubi and C. Leruste. |
| title_short | Algebraic topology via differential geometry / |
| title_sort | algebraic topology via differential geometry |
| topic | Algebraic topology. http://id.loc.gov/authorities/subjects/sh85003438 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Topologie algébrique. Géométrie différentielle. MATHEMATICS Algebra Linear. bisacsh Algebraic topology fast Geometry, Differential fast Algebraische Topologie gnd http://d-nb.info/gnd/4120861-4 DeRham-Kohomologie gnd http://d-nb.info/gnd/4352640-8 Geometrie gnd http://d-nb.info/gnd/4020236-7 Mannigfaltigkeit gnd http://d-nb.info/gnd/4037379-4 Topologische Algebra gnd http://d-nb.info/gnd/4377377-1 Differenzierbare Mannigfaltigkeit gnd http://d-nb.info/gnd/4012269-4 Geometria diferencial (textos avançados) larpcal Topologia algébrica. larpcal Cohomologia. larpcal Topologie algébrique. ram Géométrie différentielle. ram |
| topic_facet | Algebraic topology. Geometry, Differential. Topologie algébrique. Géométrie différentielle. MATHEMATICS Algebra Linear. Algebraic topology Geometry, Differential Algebraische Topologie DeRham-Kohomologie Geometrie Mannigfaltigkeit Topologische Algebra Differenzierbare Mannigfaltigkeit Geometria diferencial (textos avançados) Topologia algébrica. Cohomologia. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552511 |
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