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| Gilkey P.B. — Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem |
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| Предметный указатель |
 186
A-roof (A) genus 99
Absolute boundary conditions for the de Rham complex 243
Algebra of operators 13
Allard, William 45
Almost complex structure 180
Arithmetic genus 190 200
Arzela — Ascoli theorem 8
Asymptotic expansion of symbol 51
Asymptotics of elliptic boundary conditions 72
Asymptotics of heat equation 54
Atiyah — Bott index theorem 247
Atiyah — Patodi — Singer theorem 268 276
Atiyah — Singer index theorem 233
Axiomatic characterization of Chern forms 202
Axiomatic characterization of Euler forms 121
Axiomatic characterization of Pontrjagin forms 130
Bigrading exterior algebra 107
Bolt periodicity 221
Bundle of Cauchy data 70
Bundles of positive part of symbol 76
Canonical bundle 186
Cauchy data 70
Cecil  cohomology 166
Change of coordinates 25
Characteristic forms 01
Characteristic ring 93 98 103
Chern character 91. 174 217
Chern class of complex projective space 111
Chern form 91
Chern isomorphism in K-theory 217
Christoffel symbols 104
Clifford algebra 148
Clifford matrices 95
Clifford multiplication 148
Clutching functions 218
Cohomology of complex projective space 109 200
Cohomology of elliptic complex 37
Cohomology of Kaehler manifolds 195
Collared manifold 253
Compact operators 31
Complex, characteristic ring 93
Complex, projective space 109
Complex, tangent space 107
Connected sum 154
Connection 1-form 89
Continuity of operators 12
Convolution 2
Cotangent space 25
Cup product 151
Curvature of spin biuidle 172
Curvature, 2-form 90
d-bar  107
de Rham, cohomology 91 197
de Rham, complex 39 149 246
de Rham, signature and spin biuidles 172
Defect formulas 286 296
Dirac matrices 95
Dirichlet boundary conditions 71 245
Dolbeault and de Rham cohomology 197
Dolbeault complex 183
Donnelly Theorem 293
Double suspension 220
Dual norm 30
Elliptic, boundary conditions 72
Elliptic, complex 37
Elliptic, operators 23
| Eta function 81 258 263
Eta invariant 258 270
Euler form 100 121 174 308
Euler — Poincare characteristic 246
Euler, characteristic of elliptic complex 37
Exterior, algebra 148
Exterior, multiplication 39 148
Flat K-theory 298
Form valued polynomial 129
Fourier transform 3
Fredholm index 32
Fredholm operators 32
Resolvant of operator 52
Restriction of invariant 120 255
Riemann zeta function 80
Riemann — Roch theorem 189 202
Ring of invariant polynomials 119
Schwartz class 2
Secondary characteristic classes 273
Serre duality 199
Shape operator 251
Shuffle formulas 313
Signature of projective space 153
Signature, complex 150
Signature, spin and de Rham bundles 172
Signature, tangential operator 261
Signature, theorem 154
Simple covers 166
Singer’s conjecture for the Euler form 308
Snaith’s Theorem 305
Sobolev, lemma 7
Sobolev, spaces 6
Spectral flow 273
Spectral geometry 331
Spectrum of compact operator 42
Spectrum of self-adjoint elliptic operator 43
Sphere, bundle K-theory 267
Sphere, Chern character 96
Sphere, Euler form 101
Sphere, K-theory 221
Spherical space form 295 333
Spin and other elliptic complexes 172
Spin, complex 176
Spin, group 159
Spin, structures 165
Spin, structures on projective spaces 170
Spinors 159
Splitting principal 190
Stable isomorphism of vector bundles 216
Stationary phase 64
Stieffel — Whitney classes 167
Suspension of symbol 224
Suspension of topological space 215
Symbol de Rham complex 40
Symbol of operator on a manifold 25
Symbol, Dolbeault complex 184
Symbol, spin complex 176
Tangential operator signature complex 261
Tautological bundle of  109 195
Todd form 97 114 236
Topological charge 223
Trace heat operator 47
Transgression 92 252
U(n), homotopy groups of 221
Weyl spanning set 121
Weyl’s theorem on invariants of orthogonal group 132
Zeta function 80
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