Seminar on the Atiyah-Singer Index Theorem

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Seminar on the Atiyah-Singer Index Theorem

Edited by: Richard S. Palais

Language: English

Published/Copyright: 1966

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This book is in the series

Volume 57 | Annals of Mathematics Studies

About this book

A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies series

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.

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Topics

Mathematics Geometry and Topology

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	v
PREFACE Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	ix
CHAPTER I. STATEMENT OF THE THEOREM OUTLINE OF THE PROOF A. Borel Requires Authentication Unlicensed Licensed Download PDF	1
CHAPTER II. REVIEW OF K-THEORY Robert Solovay Requires Authentication Unlicensed Licensed Download PDF	13
CHAPTER III. THE TOPOLOGICAL INDEX OF AN OPERATOR ASSOCIATED TO A G-STRUCTURE Robert Solovay Requires Authentication Unlicensed Licensed Download PDF	27
CHAPTER IV. DIFFERENTIAL OPERATORS ON VECTOR BUNDLES Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	51
CHAPTER V. ANALYTICAL INDICES OF SOME CONCRETE OPERATORS Robert M. Solovay Requires Authentication Unlicensed Licensed Download PDF	95
CHAPTER VI. REVIEW OF FUNCTIONAL ANALYSIS Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	107
CHAPTER VII. FREDHDIM OPERATORS Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	119
CHAPTER VIII. CHAINS OP HILBERTIAN SPACES Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	125
CHAPTER IX. THE DISCRETE SOBOLEV CHAIN OF A VECTOR BUNDLE Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	147
CHAPTER X. THE CONTINUOUS SOBOLEV CHAIN OF A VECTOR BUNDLE Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	155
CHAPTER XI. THE SEELEY ALGEBRA Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	175
CHAPTER XII. HOMOTOPY INVARIANCE OF THE INDEX Richard S. Palaie Requires Authentication Unlicensed Licensed Download PDF	185
CHAPTER XIII. WHITNEY SUMS Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	191
CHAPTER XIV. TENSOR PRODUCTS Richard S. Palais Requires Authentication Unlicensed Licensed Download PDF	197
CHAPTER XV. DEFINITION OF i_a AND i_t ON K(M) Robert M. Solovay Requires Authentication Unlicensed Licensed Download PDF	215
CHAPTER XVI. CONSTRUCTION OF Int_k R. S. Palais and R. T. Seeley Requires Authentication Unlicensed Licensed Download PDF	235
CHAPTER XVII. COBORDISM INVARIANCE OP THE ANALYTICAL INDEX R. S. Palais and R. T. Seeley Requires Authentication Unlicensed Licensed Download PDF	285
CHAPTER XVIII. BORDISM GROUPS OF BUNDLES E. E. Floyd Requires Authentication Unlicensed Licensed Download PDF	303
CHAPTER XIX. THE INDEX THEOREM: APPLICATIONS Robert M. Solovay Requires Authentication Unlicensed Licensed Download PDF	313
APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY M. F. Atiyah Requires Authentication Unlicensed Licensed Download PDF	337
APPENDIX II. NON-STABLE CHARACTERISTIC CLASSES AND THE TOPOLOGICAL INDEX OP CLASSICAL ELLIPTIC OPERATORS Weishu Shih Requires Authentication Unlicensed Licensed Download PDF	353
Backmatter Requires Authentication Unlicensed Licensed Download PDF	368

Publishing information

Pages and Images/Illustrations in book

eBook published on:

March 2, 2016

eBook ISBN:

9781400882045

Pages and Images/Illustrations in book

Main content:

376

https://doi.org/10.1515/9781400882045

eBook ISBN: 9781400882045

Keywords for this book

Theorem; Atiyah–Singer index theorem; Elliptic operator; Differential operator; Normal bundle; Homotopy; Fiber bundle; Riemann–Roch theorem; Algebraic topology; Isomorphism class; Sobolev inequality; K-theory; Complex vector bundle; H-cobordism; Division by zero; Uniqueness theorem; Orientability; Grothendieck group; Projection (mathematics); Exact sequence; Euler class; Banach space; Characteristic class; Cohomology; Partial differential equation; Submanifold; Existential quantification; L-theory; Automorphism; Cokernel; Ring (mathematics); Fredholm operator; Chern class; Jet bundle; Principal bundle; Sign convention; Tangent bundle; Todd class; Arf invariant; Hilbert space; Special case; Asymptotic expansion; Elliptic partial differential equation; Equivalence class; Bounded operator; Homomorphism; Subring; Dimension (vector space); Differentiable manifold; Hodge theory; Boundary value problem; Disjoint union; Surjective function; Polynomial ring; Linear map; Functional analysis; Topological vector space; Singular integral; Formal power series; Robert M. Solovay; Summation; Michael Atiyah; Polynomial; Subgroup; Axiom; Symmetric bilinear form; Fourier transform; Tensor product; Symmetric function; Euclidean space

Audience(s) for this book

College/higher education;Professional and scholarly;

Seminar on the Atiyah-Singer Index Theorem

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