From calculus to cohomology: de Rham cohomology and characteristic classes
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2001
|
| Edition: | Repr., transferred to digital print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 286 S. graph. Darst. |
| ISBN: | 0521580595 0521589568 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface
.........................................
vii
Chapter
1
Introduction
.............................. 1
Chapter
2
The Alternating Algebra
.......................7
Chapter
3 de Rham
Cohomology
....................... 15
Chapter
4
Chain Complexes and their Cohomology
............ 25
Chapter
5
The Mayer-Vietoris Sequence
.................. 33
Chapter
6
Homotopy
.............................. 39
Chapter
7
Applications of
de Rham
Cohomology
............. 47
Chapter
8
Smooth Manifolds
......................... 57
Chapter
9
Differential Forms on Smoth Manifolds
............. 65
Chapter
10
Integration on Manifolds
..................... 83
Chapter
11
Degree, Linking Numbers and Index of Vector Fields
..... 97
Chapter
12
The
Poincaré-Hopf
Theorem
...................113
Chapter
13
Poincaré
Duality
..........................127
Chapter
14
The Complex
Projective
Space CP
...............139
Chapter
15
Fiber Bundles and Vector Bundles
................147
Chapter
16
Operations on Vector Bundles and their Sections
.......157
Chapter
17
Connections and Curvature
....................167
Chapter
18
Characteristic Classes of Complex Vector Bundles
......181
Chapter
19
The
Euler
Class
...........................193
Chapter
20
Cohomology of
Projective
and Grassmannian Bundles
.... 199
Chapter
21
Thorn Isomorphism and the General Gauss-Bonnet Formula
.211
Appendix A Smooth Partition of Unity
.....................221
Appendix
В
Invariant Polynomials
.......................227
Appendix
С
Proof of Lemmas
12.12
and
12.13................233
Appendix
D
Exercises
..............................243
References
......................................281
Index
.........................................283
|
| adam_txt |
Contents
Preface
.
vii
Chapter
1
Introduction
. 1
Chapter
2
The Alternating Algebra
.7
Chapter
3 de Rham
Cohomology
. 15
Chapter
4
Chain Complexes and their Cohomology
. 25
Chapter
5
The Mayer-Vietoris Sequence
. 33
Chapter
6
Homotopy
. 39
Chapter
7
Applications of
de Rham
Cohomology
. 47
Chapter
8
Smooth Manifolds
. 57
Chapter
9
Differential Forms on Smoth Manifolds
. 65
Chapter
10
Integration on Manifolds
. 83
Chapter
11
Degree, Linking Numbers and Index of Vector Fields
. 97
Chapter
12
The
Poincaré-Hopf
Theorem
.113
Chapter
13
Poincaré
Duality
.127
Chapter
14
The Complex
Projective
Space CP"
.139
Chapter
15
Fiber Bundles and Vector Bundles
.147
Chapter
16
Operations on Vector Bundles and their Sections
.157
Chapter
17
Connections and Curvature
.167
Chapter
18
Characteristic Classes of Complex Vector Bundles
.181
Chapter
19
The
Euler
Class
.193
Chapter
20
Cohomology of
Projective
and Grassmannian Bundles
. 199
Chapter
21
Thorn Isomorphism and the General Gauss-Bonnet Formula
.211
Appendix A Smooth Partition of Unity
.221
Appendix
В
Invariant Polynomials
.227
Appendix
С
Proof of Lemmas
12.12
and
12.13.233
Appendix
D
Exercises
.243
References
.281
Index
.283 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:38:28Z |
| indexdate | 2024-07-09T21:14:47Z |
| institution | BVB |
| isbn | 0521580595 0521589568 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016462495 |
| oclc_num | 255237765 |
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| physical | VII, 286 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Cambridge Univ. Press |
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| spelling | Madsen, Ib Verfasser aut From calculus to cohomology de Rham cohomology and characteristic classes Ib Madsen and Jørgen Tornehave Repr., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2001 VII, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier DeRham-Kohomologie (DE-588)4352640-8 gnd rswk-swf DeRham-Kohomologie (DE-588)4352640-8 s DE-604 Tornehave, Jørgen Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016462495&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Madsen, Ib Tornehave, Jørgen From calculus to cohomology de Rham cohomology and characteristic classes DeRham-Kohomologie (DE-588)4352640-8 gnd |
| subject_GND | (DE-588)4352640-8 |
| title | From calculus to cohomology de Rham cohomology and characteristic classes |
| title_auth | From calculus to cohomology de Rham cohomology and characteristic classes |
| title_exact_search | From calculus to cohomology de Rham cohomology and characteristic classes |
| title_exact_search_txtP | From calculus to cohomology de Rham cohomology and characteristic classes |
| title_full | From calculus to cohomology de Rham cohomology and characteristic classes Ib Madsen and Jørgen Tornehave |
| title_fullStr | From calculus to cohomology de Rham cohomology and characteristic classes Ib Madsen and Jørgen Tornehave |
| title_full_unstemmed | From calculus to cohomology de Rham cohomology and characteristic classes Ib Madsen and Jørgen Tornehave |
| title_short | From calculus to cohomology |
| title_sort | from calculus to cohomology de rham cohomology and characteristic classes |
| title_sub | de Rham cohomology and characteristic classes |
| topic | DeRham-Kohomologie (DE-588)4352640-8 gnd |
| topic_facet | DeRham-Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016462495&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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