THE ATIYAH-SINGER INDEX THEOREM
CHAPTER 1 PSEUDO-DI?ERENTIAL OPERATORS INTRODUCTION 11 FOURIER TRANSFORM, SCHWARTZ CLASS, AND SOBOLEV SPACES 12 PSEUDO-DI?ERENTIAL OPERATORS ON RM 13 ELLIPTICITY AND PSEUDO-DI?ERENTIAL OPERATORS ON MANIFOLDS 14 FREDHOLM OPERATORS AND THE INDEX OF A FREDHOLM OPERATOR ELLIPTIC COMPLEXES, THE HODGE DECOMPOSITION THEOREM, AND POINCAR´E DUALITY 16 THE HEAT EQUATION 17 LOCAL FORMULA FOR THE INDEX OF AN ELLIPTIC OPERATOR 18 LEFSCHETZ FIXED POINT THEOREMS 19 ELLIPTIC BOUNDARY VALUE PROBLEMS 110 ETA AND ZETA FUNCTIONS CHAPTER 2 CHARACTERISTIC CLASSES INTRODUCTION 21 CHARACTERISTIC CLASSES OF A COMPLEX BUNDLE CHARACTERISTIC CLASSES OF A REAL VECTOR BUNDLE PONTRJAGIN AND EULER CLASSES 23 CHARACTERISTIC CLASSES OF COMPLEX PROJECTIVE SPACE 24 THE GAUSS-BONNET THEOREM INVARIANCE THEORY AND THE PONTRJAGIN CLASSES OF THE TANGENT BUNDLE INVARIANCE THEORY AND MIXED CHARACTERISTIC CLASSES OF THE TANGENT SPACE AND OF A COE?CIENT BUNDLE CHAPTER 3 THE INDEX THEOREM INTRODUCTION 31 THE HIRZEBRUCH SIGNATURE FORMULA 32 SPINORS AND THEIR REPRESENTATIONS 33 SPIN STRUCTURES ON VECTOR BUNDLES 34 THE SPIN COMPLEX 35 THE RIEMANN-ROCH THEOREM FOR ALMOST COMPLEX MANIFOLDS 36 A REVIEW OF KAEHLER GEOMETRY AN AXIOMATIC CHARACTERIZATION OF THE CHARACTERISTIC FORMS FOR HOLOMORPHIC MANIFOLDS WITH KAEHLER METRICS 38 THE CHERN ISOMORPHISM AND BOTT PERIODICITY 39 THE ATIYAH-SINGER INDEX THEOREM CHAPTER 4 GENERALIZED INDEX THEOREMS AND SPECIAL TOPICS INTRODUCTION 41 THE DE RHAM COMPLEX FOR MANIFOLDS WITH BOUNDARY 42 THE GAUSS-BONNET THEOREM FOR MANIFOLDS WITH BOUNDARY 43 THE REGULARITY AT S = 0 OF THE ETA INVARIANT 44 THE ETA INVARIANT WITH COE?CIENTS IN A LOCALLY FLAT BUNDLE 45 LEFSCHETZ FIXED POINT FORMULAS 46 THE ETA INVARIANT AND THE K-THEORY OF SPHERICAL SPACE FORMS 47 SINGER’S CONJECTURE FOR THE EULER FORM 48 LOCAL FORMULAS FOR THE INVARIANTS OF THE HEAT EQUATION 49 SPECTRAL GEOMETRY CHAPTER