Index Theory with Applications to Mathematics and Physics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
International Press
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 723 - 740 |
| Beschreibung: | XXII, 766 S. graph. Darst. |
| ISBN: | 9781571462640 |
Internformat
MARC
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| 100 | 1 | |a Bleecker, David |d 1948- |e Verfasser |0 (DE-588)1017094063 |4 aut | |
| 245 | 1 | 0 | |a Index Theory with Applications to Mathematics and Physics |c David D. Bleecker ; Bernhelm Booß-Bavnbek |
| 264 | 1 | |a Boston |b International Press |c 2013 | |
| 300 | |a XXII, 766 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 723 - 740 | ||
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| 689 | 0 | 1 | |a Globale Analysis |0 (DE-588)4021285-3 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026105301 | ||
Datensatz im Suchindex
| _version_ | 1804150522176864256 |
|---|---|
| adam_text | Titel: Index theory with applications to mathematics and physics
Autor: Bleecker, David
Jahr: 2013
Contents
Synopsis
xi
Preface
xvi
Part
I.
Operators
with
Index
and
Homotopy
Theory
1
Chapter
1.
Fredholm
Operators
2
1.
Hierarchy
of
Mathematical
Objects
2
2.
The
Concept
of
Fredholm
Operator
3
3.
Algebraic
Properties.
Operators
of
Finite
Rank.
The
Snake
Lemma
5
4.
Operators
of
Finite
Rank
and
the
Fredholm
Integral
Equation
9
5.
The
Spectra
of
Bounded
Linear
Operators:
Basic
Concepts
10
Chapter
2.
Analytic
Methods.
Compact
Operators
12
1.
Analytic
Methods.
The
Adjoint
Operator
12
2.
Compact
Operators
18
3.
The
Classical
Integral
Operators
25
4.
The
Fredholm
Alternative
and
the
Riesz
Lemma
26
5.
Sturm-Liouville
Boundary
Value
Problems
28
6.
Unbounded
Operators
34
7.
Trace
Class
and
Hilbert-Schmidt
Operators
53
Chapter
3.
Fredholm
Operator
Topology
63
1.
The
Calkin
Algebra
63
2.
Perturbation
Theory
65
3.
Homotopy
Invariance
of
the
Index
68
4.
Homotopies
of
Operator-Valued
Functions
72
5.
The
Theorem
of
Kuiper
77
6.
The
Topology
of
T
81
7.
The
Construction
of
Index
Bundles
82
8.
The
Theorem
of
Atiyah-Jänich
88
9.
Determinant
Line
Bundles
91
10.
Essential
Unitary
Equivalence
and
Spectral
Invariants
108
Chapter
4.
Wiener-Hopf
Operators
120
1.
The
Reservoir
of
Examples
of
Fredholm
Operators
120
2.
Origin
and
Fundamental
Significance
of
Wiener-Hopf
Operators
121
3.
The
Characteristic
Curve
of
a
Wiener-Hopf
Operator
122
4.
Wiener-Hopf
Operators
and
Harmonic
Analysis
123
5.
The
Discrete
Index
Formula.
The
Case
of
Systems
125
6.
The
Continuous
Analogue
129
vii
CONTENTS
viii
Part
II.
Analysis
on
Manifolds
133
Chapter
5.
Partial
Differential
Equations
in
Euclidean
Space
134
1.
Linear
Partial
Differential
Equations
134
2.
Elliptic
Differential
Equations
137
3.
Where
Do
Elliptic
Differential
Operators
Arise?
139
4.
Boundary-Value
Conditions
141
5.
Main
Problems
of
Analysis
and
the
Index
Problem
143
6.
Numerical
Aspects
143
7.
Elementary
Examples
144
Chapter
6.
Differential
Operators
over
Manifolds
156
1.
Differentiable
Manifolds
—
Foundations
157
2.
Geometry
of
C°°
Mappings
160
3.
Integration
on
Manifolds
166
4.
Exterior
Differential
Forms
and
Exterior
Differentiation
171
5.
Covariant
Differentiation,
Connections
and
Parallelity
176
6.
Differential
Operators
on
Manifolds
and
Symbols
181
7.
Manifolds
with
Boundary
190
Chapter
7.
Sobolev
Spaces
(Crash
Course)
193
1.
Motivation
193
2.
Definition
194
3.
The
Main
Theorems
on
Sobolev
Spaces
200
4.
Case
Studies
203
Chapter
8.
Pseudo-Differential
Operators
206
1.
Motivation
206
2.
Canonical
Pseudo-Differential
Operators
210
3.
Principally
Classical
Pseudo-Differential
Operators
214
4.
Algebraic
Properties
and
Symbolic
Calculus
228
5.
Normal
(Global)
Amplitudes
231
Chapter
9.
Elliptic
Operators
over
Closed
Manifolds
237
1.
Mapping
Properties
of
Pseudo-Differential
Operators
237
2.
Elliptic
Operators
—
Regularity
and
Fredholm
Property
239
3.
Topological
Closure
and
Product
Manifolds
242
4.
The
Topological
Meaning
of
the
Principal
Symbol
—
A
Simple
Case
Involving
Local
Boundary
Conditions
244
Part
III.
The
Atiyah-Singer
Index
Formula
251
Chapter
10.
Introduction
to
Topological
R-Theory
252
1.
Winding
Numbers
252
2.
The
Topology
of
the
General
Linear
Group
257
3.
Elementary
R-Theory
262
4.
R-Theory
with
Compact
Support
266
5.
Proof
of
the
Periodicity
Theorem
of
R.
Bott
269
Chapter
11.
The
Index
Formula
in
the
Euclidean
Case
275
1.
Index
Formula
and
Bott
Periodicity
275
CONTENTS
ix
2.
The
Difference
Bundle
of
an
Elliptic
Operator
276
3.
The
Index
Theorem
for
Ell
c
(M
n
)
281
Chapter
12.
The
Index
Theorem
for
Closed
Manifolds
284
1.
Pilot
Study:
The
Index
Formula
for
Trivial
Embeddings
285
2.
Proof
of
the
Index
Theorem
for
Nontrivial
Normal
Bundle
287
3.
Comparison
of
the
Proofs
301
Chapter
13.
Classical
Applications
(Survey)
310
1.
Cohomological
Formulation
of
the
Index
Formula
311
2.
The
Case
of
Systems
(Trivial
Bundles)
316
3.
Examples
of
Vanishing
Index
317
4.
Euler
Characteristic
and
Signature
319
5.
Vector
Fields
on
Manifolds
325
6.
Abelian
Integrals
and
Riemann
Surfaces
329
7.
The
Theorem
of
Hirzebruch-Riemann-Roch
333
8.
The
Index
of
Elliptic
Boundary-Value
Problems
337
9.
Real
Operators
356
10.
The
Lefschetz
Fixed-Point
Formula
357
11.
Analysis
on
Symmetric
Spaces:
The
G-equivariant
Index
Theorem
360
12.
Further
Applications
362
Part
IV.
Index
Theory
in
Physics
and
the
Local
Index
Theorem
363
Chapter
14.
Physical
Motivation
and
Overview
364
1.
Classical
Field
Theory
365
2.
Quantum
Theory
373
Chapter
15.
Geometric
Preliminaries
394
1.
Principal
G-Bundles
394
2.
Connections
and
Curvature
396
3.
Equivariant
Forms
and
Associated
Bundles
400
4.
Gauge
Transformations
409
5.
Curvature
in
Riemannian
Geometry
414
6.
Bochner-Weitzenbock
Formulas
434
7.
Characteristic
Classes
and
Curvature
Forms
443
8.
Holonomy
455
Chapter
16.
Gauge
Theoretic
Instantons
460
1.
The
Yang-Mills
Functional
460
2.
Instantons
on
Euclidean
4-Space
466
3.
Linearization
of
the
Moduli
Space
of
Self-dual
Connections
489
4.
Manifold
Structure
for
Moduli
of
Self-dual
Connections
496
Chapter
17.
The
Local
Index
Theorem
for
Twisted
Dirac
Operators
513
1.
Clifford
Algebras
and
Spinors
513
2.
Spin
Structures
and
Twisted
Dirac
Operators
525
3.
The
Spinorial
Heat
Kernel
538
4.
The
Asymptotic
Formula
for
the
Heat
Kernel
549
5.
The
Local
Index
Formula
576
CONTENTS
6.
The
Index
Theorem
for
Standard
Geometric
Operators
594
Chapter
18.
Seiberg-Witten
Theory
643
1.
Background
and
Survey
643
2.
Spin
c
Structures
and
the
Seiberg-Witten
Equations
655
3.
Generic
Regularity
of
the
Moduli
Spaces
663
4.
Compactness
of
Moduli
Spaces
and
the
Definition
of
S-W
Invariants
685
Appendix
A.
Fourier
Series
and
Integrals
-
Fundamental
Principles
705
1.
Fourier
Series
705
2.
The
Fourier
Integral
707
Appendix
B.
Vector
Bundles
712
1.
Basic
Definitions
and
First
Examples
712
2.
Homotopy
Equivalence
and
Isomorphy
716
3.
Clutching
Construction
and
Suspension
718
Bibliography
723
Index
of
Notation
741
Index
of
Names/Authors
749
Subject
Index
757
|
| any_adam_object | 1 |
| author | Bleecker, David 1948- Booss-Bavnbek, Bernhelm 1941- |
| author_GND | (DE-588)1017094063 (DE-588)108280470 |
| author_facet | Bleecker, David 1948- Booss-Bavnbek, Bernhelm 1941- |
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| bvnumber | BV041129450 |
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| ctrlnum | (OCoLC)862797257 (DE-599)BVBBV041129450 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041129450 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:15Z |
| institution | BVB |
| isbn | 9781571462640 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026105301 |
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| physical | XXII, 766 S. graph. Darst. |
| publishDate | 2013 |
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| publisher | International Press |
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| spelling | Bleecker, David 1948- Verfasser (DE-588)1017094063 aut Index Theory with Applications to Mathematics and Physics David D. Bleecker ; Bernhelm Booß-Bavnbek Boston International Press 2013 XXII, 766 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 723 - 740 Indextheorie (DE-588)4161489-6 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Indextheorie (DE-588)4161489-6 s Globale Analysis (DE-588)4021285-3 s DE-604 Booss-Bavnbek, Bernhelm 1941- Verfasser (DE-588)108280470 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026105301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bleecker, David 1948- Booss-Bavnbek, Bernhelm 1941- Index Theory with Applications to Mathematics and Physics Indextheorie (DE-588)4161489-6 gnd Globale Analysis (DE-588)4021285-3 gnd |
| subject_GND | (DE-588)4161489-6 (DE-588)4021285-3 |
| title | Index Theory with Applications to Mathematics and Physics |
| title_auth | Index Theory with Applications to Mathematics and Physics |
| title_exact_search | Index Theory with Applications to Mathematics and Physics |
| title_full | Index Theory with Applications to Mathematics and Physics David D. Bleecker ; Bernhelm Booß-Bavnbek |
| title_fullStr | Index Theory with Applications to Mathematics and Physics David D. Bleecker ; Bernhelm Booß-Bavnbek |
| title_full_unstemmed | Index Theory with Applications to Mathematics and Physics David D. Bleecker ; Bernhelm Booß-Bavnbek |
| title_short | Index Theory with Applications to Mathematics and Physics |
| title_sort | index theory with applications to mathematics and physics |
| topic | Indextheorie (DE-588)4161489-6 gnd Globale Analysis (DE-588)4021285-3 gnd |
| topic_facet | Indextheorie Globale Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026105301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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