Atiyah-Singer index theorem: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Delhi
Hindustan Book Agency
2013
|
| Schriftenreihe: | Texts and readings in mathematics
69 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 267 S. |
| ISBN: | 9789380250540 |
Internformat
MARC
| LEADER | 00000nam a22000002cb4500 | ||
|---|---|---|---|
| 001 | BV041411703 | ||
| 003 | DE-604 | ||
| 005 | 20140730 | ||
| 007 | t | ||
| 008 | 131112s2013 |||| 00||| eng d | ||
| 020 | |a 9789380250540 |9 978-938-025-054-0 | ||
| 035 | |a (OCoLC)869852724 | ||
| 035 | |a (DE-599)BSZ393633748 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-355 | ||
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 100 | 1 | |a Mukherjee, Amiya |e Verfasser |0 (DE-588)142817686 |4 aut | |
| 245 | 1 | 0 | |a Atiyah-Singer index theorem |b an introduction |c Amiya Mukherjee |
| 264 | 1 | |a New Delhi |b Hindustan Book Agency |c 2013 | |
| 300 | |a XII, 267 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts and readings in mathematics |v 69 | |
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| 830 | 0 | |a Texts and readings in mathematics |v 69 |w (DE-604)BV011380811 |9 69 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026858985&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026858985 | ||
Datensatz im Suchindex
| _version_ | 1804151523257614336 |
|---|---|
| adam_text | Contents
Chapter
1. K-Theory
1
1.1.
Vector bundles
1
1.2.
Classification of bundles
5
1.3.
The functors
К
and
К
8
1.4.
Clutching construction
12
1.5.
Relative K-theory and long exact sequence
15
1.6.
K-theory with compact support
20
1.7.
Products in /C-theory
21
1.8.
Complexes of vector bundles
24
1.9.
Multiplication in L (X,A)
30
1.10.
Complexes with compact support
32
Chapter
2.
Fredholm
Operators and
Atiyah-Jänich
Theorem
35
2.1.
Fredholm
operators
35
2.2.
Compact operators
38
2.3.
Index bundle
42
2.4.
Atiyah-Jänich
theorem
46
2.5.
Kuiper s theorem
47
Chapter
3.
Bott
Periodicity and Thom Isomorphism
53
3.1.
Toeplitz operator
53
3.2.
K-Theory of complex
projective
spaces
63
3.3.
Exterior power operations
65
3.4.
Thom isomorphism
70
Chapter
4.
Pseudo-Diiferential Operators
76
4.1.
Sobolev spaces
76
4.2.
Differential operators on manifolds
84
4.3.
Pseudo-differential operators on Rn
87
4.4.
Fourier integral operator
95
4.5.
Elliptic pseudo-differential operators
105
4.6.
Pseudo-differential operators on manifolds
108
4.7.
Heat operator
112
Chapter
5.
Characteristic Classes and Chern-Weil Construction
120
5.1.
Chern classes
120
5.2.
Connection and curvature
132
xii CONTENTS
5.3. Chern-Weil
construction
141
5.4. Pontrjagin
classes
of a real bundle
146
Chapter
6.
Spin Structure and Dirac Operator
148
6.1.
Clifford algebras
148
6.2.
Structure of complexified Clifford algebras
159
6.3.
The spinor representations
162
6.4.
Spin structures
166
6.5.
Dirac operators
168
6.6.
Hodge theory and Dirac operator.
172
Chapter
7.
Equi
variant K-Theory
178
7.1.
Elementary theory
178
7.2.
Equivariant
Bott
periodicity
190
7.3.
Equivariant Thom isomorphism theorem
195
7.4.
Localization theorem
196
Chapter
8.
The Index Theorem
200
8.1.
Formulation of the index theorem
200
8.2.
Excision property
208
8.3.
Multiplicative property
209
8.4.
Equivariant index
212
8.5.
Multiplicative property for sphere bundle
218
8.6.
Completion of the proof of the index theorem
222
8.7.
Equivariant index theorem
223
Chapter
9.
Cohomological Formulation of the Index Theorem
226
9.1.
Splitting principle for real bundles
226
9.2.
Multiplicative sequences
227
9.3.
Examples of multiplicative sequences
229
9.4.
Thom isomorphism in cohomology and if-theory
232
9.5.
The class
μ(Ε)
235
9.6.
Topological index in cohomological form
236
9.7.
Sequence of differential operators
241
9.8.
Euler
characteristic operator
242
9.9.
Hirzebruch signature theorem
244
9.10.
Riemann-Roch-Hirzebruch Theorem
247
9.11.
Dirac operator
251
9.12.
Atiyah-Segal-Singer fixed point theorem
254
Bibliography
261
Index
265
This monograph is a thorough introduction to the Atiyah-Singer
index theorem tor effiptic operators on compact manifolds without
boundary. The main theme is the classical index theorem and some
of its applications, but not the subsequent developments and
simplifications of the theory. The book is designed for
a compiete
proof of the K-theoretic index theorem and its representation in
terms of cohomological characteristic classes. An effort has been
made to make the demands on the knowledge of background
material as modest as possible by supplying the proofs of almost
every result. The applications include Hirzebruch signature
theorem, Riemann-Roch-Hirzebruch theorem, Atiyah-Segal-Singer
fixed point theorem, etc.
|
| any_adam_object | 1 |
| author | Mukherjee, Amiya |
| author_GND | (DE-588)142817686 |
| author_facet | Mukherjee, Amiya |
| author_role | aut |
| author_sort | Mukherjee, Amiya |
| author_variant | a m am |
| building | Verbundindex |
| bvnumber | BV041411703 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)869852724 (DE-599)BSZ393633748 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041411703 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:56:10Z |
| institution | BVB |
| isbn | 9789380250540 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026858985 |
| oclc_num | 869852724 |
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| owner | DE-188 DE-355 DE-BY-UBR |
| owner_facet | DE-188 DE-355 DE-BY-UBR |
| physical | XII, 267 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Hindustan Book Agency |
| record_format | marc |
| series | Texts and readings in mathematics |
| series2 | Texts and readings in mathematics |
| spelling | Mukherjee, Amiya Verfasser (DE-588)142817686 aut Atiyah-Singer index theorem an introduction Amiya Mukherjee New Delhi Hindustan Book Agency 2013 XII, 267 S. txt rdacontent n rdamedia nc rdacarrier Texts and readings in mathematics 69 Indextheorem (DE-588)4140055-0 gnd rswk-swf Indextheorem (DE-588)4140055-0 s DE-604 Texts and readings in mathematics 69 (DE-604)BV011380811 69 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026858985&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026858985&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mukherjee, Amiya Atiyah-Singer index theorem an introduction Texts and readings in mathematics Indextheorem (DE-588)4140055-0 gnd |
| subject_GND | (DE-588)4140055-0 |
| title | Atiyah-Singer index theorem an introduction |
| title_auth | Atiyah-Singer index theorem an introduction |
| title_exact_search | Atiyah-Singer index theorem an introduction |
| title_full | Atiyah-Singer index theorem an introduction Amiya Mukherjee |
| title_fullStr | Atiyah-Singer index theorem an introduction Amiya Mukherjee |
| title_full_unstemmed | Atiyah-Singer index theorem an introduction Amiya Mukherjee |
| title_short | Atiyah-Singer index theorem |
| title_sort | atiyah singer index theorem an introduction |
| title_sub | an introduction |
| topic | Indextheorem (DE-588)4140055-0 gnd |
| topic_facet | Indextheorem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026858985&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026858985&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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