Atiyah Singer Index Theorem An IntroductionAtiyah Singer Index Theorem An Introduction

2013-10-302013-10-30 Amiya MukherjeeAmiya Mukherjee

The book is designed for a complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes.

Author: Amiya Mukherjee

Publisher: Springer

ISBN: 9789386279606

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Page: 276

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This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only 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 complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.

Seminar on Atiyah Singer Index Theorem AM 57 Volume 57Seminar on Atiyah Singer Index Theorem AM 57 Volume 57

2016-03-022016-03-02 Richard S. PalaisRichard S. Palais

The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.

Author: Richard S. Palais

Publisher: Princeton University Press

ISBN: 9781400882045

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Page: 376

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The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.

Invariance TheoryInvariance Theory

2018-05-022018-05-02 Peter B. GilkeyPeter B. Gilkey

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex.

Author: Peter B. Gilkey

Publisher: CRC Press

ISBN: 9781351436427

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Page: 536

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This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.

Index Theorem 1Index Theorem 1

20072007 M. FurutaM. Furuta

The Atiyah-Singer index theorem is a remarkable result that allows one to compute the space of solutions of a linear elliptic partial differential operator on a manifold in terms of purely topological data related to the manifold and the ...

Author: M. Furuta

Publisher: American Mathematical Soc.

ISBN: 0821820974

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Page: 205

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The Atiyah-Singer index theorem is a remarkable result that allows one to compute the space of solutions of a linear elliptic partial differential operator on a manifold in terms of purely topological data related to the manifold and the symbol of the operator. First proved by Atiyah and Singer in 1963, it marked the beginning of a completely new direction of research in mathematics with relations to differential geometry, partial differential equations, differential topology, K-theory, physics, and other areas. The author's main goal in this volume is to give a complete proof of the index theorem. The version of the proof he chooses to present is the one based on the localization theorem. The prerequisites include a first course in differential geometry, some linear algebra, and some facts about partial differential equations in Euclidean spaces.