Index theorem 1:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, RI
American Mathematical Society
2007
|
| Series: | Translations of mathematical monographs
235 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Japan. übers. Includes bibliographical references and index |
| Physical Description: | XVII, 205 S. Ill. 22 cm |
| ISBN: | 9780821820971 |
Staff View
MARC
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| 100 | 1 | |a Furuta, Mikio |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Index theorem 1 |c Mikio Furuta ; translated by Kaoru Ono |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2007 | |
| 300 | |a XVII, 205 S. |b Ill. |c 22 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 235 | |
| 490 | 0 | |a Iwanami series in modern mathematics | |
| 500 | |a Aus d. Japan. übers. | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Análise global |2 larpcal | |
| 650 | 4 | |a Index theorems | |
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Record in the Search Index
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| adam_text | Contents
Preface
vii
Outline
of the Theory and Perspective
ix
Chapter
1.
Prelude
1
1.
What Is the Index?
1
2.
What Is the Atiyah-Singer Index Theorem?
11
3. 1
-Dimensional Case
20
Chapter
2.
Manifolds, Vector Bundles and Elliptic Complexes
27
1.
Differential Forms with Compact Support and Their
Integration
27
2.
Embeddings of Manifolds and Vector Bundles to Trivial
Objects
30
3.
Clifford Modules and Operators of Dirac Type
34
4.
Elliptic Differential Operators Appearing in Geometry
and Operators of Dirac Type
54
Chapter
3.
Index and Its Localization
63
1.
Definition of the Index of Operators of Dirac Type on
Closed Manifolds
63
2.
Definition of the Index of Operators of Dirac Type on
Open Manifolds
65
3.
The Excision Theorem and Topological
Invariance
of the
Index
76
4.
Products of Operators of Dirac Type and Their Indices
79
5.
Supersymmetric Harmonic Oscillator and the
de Rham
Complex on the Euclidean Space
81
Chapter
4.
Examples of the Localization of the Index
93
1.
The
Poincaré-Hopf
Theorem and the Morse Inequality
93
2.
Riemann-Roch Theorem on Riemann Surfaces
104
vi
CONTENTS
3.
Mod
2
Index of Spin Structures on Riemann Surfaces
107
4.
The Case with a Group Action: Lefschetz Formula
116
Chapter
5.
Localization of Eigenfunctions of the Operator of
Laplace Type
125
1.
Set-up
125
2.
Exponential Decay
128
3.
Preliminaries for the Calculus of Variation
131
4.
Calculus of Variations
138
5.
Oscillation of Eigenvalues and Eigenfunctions
143
6.
Modification of Operators on Ends
148
7.
The Case of Closed Manifolds: Spectral Decomposition
152
Chapter
6.
Formulation and Proof of the Index Theorem
157
1.
Strategy for Our Formulation and Proof
157
2.
Construction of the Pair on the Euclidean Space
160
3.
Invariance
of the Index: Proof
1
(The Index of the
Product)
164
4.
Invariance
of the Index: Proof
2
(Excision Theorem)
174
5.
Pairs on Even Dimensional Euclidean Spaces
174
Chapter
7.
Characteristic Classes
177
1.
Connection and Curvature
177
2.
Chern Character and Chern Classes
181
3.
Localization of Chern Character
186
4.
Thorn Class and Thorn Isomorphism
195
5.
The
Euler
Class
199
Index
203
|
| adam_txt |
Contents
Preface
vii
Outline
of the Theory and Perspective
ix
Chapter
1.
Prelude
1
1.
What Is the Index?
1
2.
What Is the Atiyah-Singer Index Theorem?
11
3. 1
-Dimensional Case
20
Chapter
2.
Manifolds, Vector Bundles and Elliptic Complexes
27
1.
Differential Forms with Compact Support and Their
Integration
27
2.
Embeddings of Manifolds and Vector Bundles to Trivial
Objects
30
3.
Clifford Modules and Operators of Dirac Type
34
4.
Elliptic Differential Operators Appearing in Geometry
and Operators of Dirac Type
54
Chapter
3.
Index and Its Localization
63
1.
Definition of the Index of Operators of Dirac Type on
Closed Manifolds
63
2.
Definition of the Index of Operators of Dirac Type on
Open Manifolds
65
3.
The Excision Theorem and Topological
Invariance
of the
Index
76
4.
Products of Operators of Dirac Type and Their Indices
79
5.
Supersymmetric Harmonic Oscillator and the
de Rham
Complex on the Euclidean Space
81
Chapter
4.
Examples of the Localization of the Index
93
1.
The
Poincaré-Hopf
Theorem and the Morse Inequality
93
2.
Riemann-Roch Theorem on Riemann Surfaces
104
vi
CONTENTS
3.
Mod
2
Index of Spin Structures on Riemann Surfaces
107
4.
The Case with a Group Action: Lefschetz Formula
116
Chapter
5.
Localization of Eigenfunctions of the Operator of
Laplace Type
125
1.
Set-up
125
2.
Exponential Decay
128
3.
Preliminaries for the Calculus of Variation
131
4.
Calculus of Variations
138
5.
Oscillation of Eigenvalues and Eigenfunctions
143
6.
Modification of Operators on Ends
148
7.
The Case of Closed Manifolds: Spectral Decomposition
152
Chapter
6.
Formulation and Proof of the Index Theorem
157
1.
Strategy for Our Formulation and Proof
157
2.
Construction of the Pair on the Euclidean Space
160
3.
Invariance
of the Index: Proof
1
(The Index of the
Product)
164
4.
Invariance
of the Index: Proof
2
(Excision Theorem)
174
5.
Pairs on Even Dimensional Euclidean Spaces
174
Chapter
7.
Characteristic Classes
177
1.
Connection and Curvature
177
2.
Chern Character and Chern Classes
181
3.
Localization of Chern Character
186
4.
Thorn Class and Thorn Isomorphism
195
5.
The
Euler
Class
199
Index
203 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:47:17Z |
| indexdate | 2024-07-09T21:15:22Z |
| institution | BVB |
| isbn | 9780821820971 |
| language | English Japanese |
| lccn | 2007060301 |
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| physical | XVII, 205 S. Ill. 22 cm |
| publishDate | 2007 |
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| publisher | American Mathematical Society |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs Iwanami series in modern mathematics |
| spelling | Furuta, Mikio Verfasser aut Index theorem 1 Mikio Furuta ; translated by Kaoru Ono Providence, RI American Mathematical Society 2007 XVII, 205 S. Ill. 22 cm txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 235 Iwanami series in modern mathematics Aus d. Japan. übers. Includes bibliographical references and index Análise global larpcal Index theorems Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Indextheorem (DE-588)4140055-0 gnd rswk-swf Indextheorem (DE-588)4140055-0 s Elliptischer Differentialoperator (DE-588)4140057-4 s DE-604 Translations of mathematical monographs 235 (DE-604)BV000002394 235 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016487046&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Furuta, Mikio Index theorem 1 Translations of mathematical monographs Análise global larpcal Index theorems Elliptischer Differentialoperator (DE-588)4140057-4 gnd Indextheorem (DE-588)4140055-0 gnd |
| subject_GND | (DE-588)4140057-4 (DE-588)4140055-0 |
| title | Index theorem 1 |
| title_auth | Index theorem 1 |
| title_exact_search | Index theorem 1 |
| title_exact_search_txtP | Index theorem 1 |
| title_full | Index theorem 1 Mikio Furuta ; translated by Kaoru Ono |
| title_fullStr | Index theorem 1 Mikio Furuta ; translated by Kaoru Ono |
| title_full_unstemmed | Index theorem 1 Mikio Furuta ; translated by Kaoru Ono |
| title_short | Index theorem 1 |
| title_sort | index theorem 1 |
| topic | Análise global larpcal Index theorems Elliptischer Differentialoperator (DE-588)4140057-4 gnd Indextheorem (DE-588)4140055-0 gnd |
| topic_facet | Análise global Index theorems Elliptischer Differentialoperator Indextheorem |
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