Topology and analysis: the Atiyah-Singer index formula and gauge-theoretic physics

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Springer-Verlag, 1985 - Mathematics - 451 pages
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Contents

OPERATORS WITH INDEX
1
Analytic Methods Compact Operators
13
The Fredholm Alternative
26
The Main Theorems
34
Families of Invertible Operators Kuipers Theorem
47
Families of Fredholm Operators Index Bundles
60
Fourier Series and Integrals Fundamental Principles
79
ANALYSIS ON MANIFOLDS
103
Elliptic BoundaryValue Systems II Survey
208
THE ATIYAHSINGER INDEX FORMULA
218
B The Topology of the General Linear Group
224
The Index Formula in the Euclidean Case
246
The Index Theorem for Closed Manifolds
256
Applications Survey
269
THE INDEX FORMULA AND GAUGETHEORETICAL PHYSICS
305
Geometric Preliminaries
331

Differential Operators over Manifolds
126
PseudoDifferential Operators
144
Sobolev Spaces Crash Course
172
Elliptic Operators over Closed Manifolds
182
Elliptic BoundaryValue Systems I Differential Operators
189
Elliptic Differential Operators of First Order with
199
GaugeTheoretic Instantons
359
What are Vector Bundles?
402
Index of Notation
428
Subject Index
441
Copyright

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