ABSTRACT

Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl

part |2 pages

Dedication

chapter |4 pages

Contents

part |2 pages

Introduction

chapter 1|14 pages

Resumé of Riemannian geometry

chapter 3|14 pages

Clifford algebras and Dirac operators

chapter 4|16 pages

The Spin groups

chapter 5|16 pages

Analytic properties o f Dirac operators

chapter 6|8 pages

Hodge theory

chapter 7|14 pages

The heat and wave equations

chapter 8|10 pages

Traces and eigenvalue asymptotics

chapter 9|14 pages

Some non-compact manifolds

chapter 10|8 pages

The Lefschetz formula

chapter 11|10 pages

The index problem

chapter 13|14 pages

Applications of the index theorem

chapter 14|10 pages

Witten’s approach to Morse theory

chapter 15|10 pages

Atiyah’s Г-index theorem