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| Berline N., Getzler E., Vergne M. — Heat Kernels and Dirac Operators |
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| Предметный указатель |
 -metric 302
 -operator 136
 -genus 50 144
-genus equivariant 213
 -endomorphism 279 310
Adjoint, formal 68 89
Affine connection 28
Almost-complex manifold 135
Anomaly formula 350
Associated bundle 15
Atiyah — Bott fixed point formula 187
Atiyah — Segal — Singer fixed point formula 196
Atiyah, M.F. 147 150 187 196 245 295 339
Baum, P. 225
Berezin integral 42 54 106 109 146 196 243
Bianchi identity 44
Bismut Laplacian 258
Bismut superconnection 332 347
Bismut, J.M. 258 282 332 338 348
Bochner — Kodaira formula 140
Borel — Weil — Bott theorem 257
Bott class 241
Bott, R. 187 224 257
Bundle, associated 15
Bundle, Clifford 113
Bundle, equivariant 16 209
Bundle, frame 15 32
Bundle, holomorphic 136
Bundle, horizontal 21
Bundle, index 281 299
Bundle, principal 15
Canonical line bundle 140
Cartan subalgebra 229
Casimir operator 172
Character formula, Kirillov 254
Character formula, Weyl 253
Characteristic class 47
Characteristic class, -genus 50 151 337
Characteristic class, Chern character 49 286
Characteristic class, equivariant 212
Characteristic class, Euler class 58 148
Characteristic class, L-genus 150
Characteristic class, Todd genus 51 152
Characteristic number, Bott's formula 225
Cheeger, J. 225
Chern character 49 286
Chern character, equivariant 212
Chern character, relative 146
Chern character, relative, equivariant 250
Chern character, relative, localized 195
Chern — Weil homomorphism 47
Chern — Weil homomorphism, equivariant 236 294 352
Chern, S.S. 59
Chevalley, C. 108 233
Chirality operator 109
Clifford algebra 103
Clifford algebra, quantization map 104
Clifford algebra, supertrace 110
Clifford algebra, symbol map 104
Clifford bundle 113
Clifford connection 117 329
Clifford module 103 114 127 325
Clifford module, equivariant 186
Clifford module, twisted 114
Clifford superconnectton 117
Coadjoint orbit, Fourier transform 228
Cohomology, de Rham 18 128 296
Cohomology, Dolbeault 139
Cohomology, equivariant 209
Complex manifold 135
Connection 20
Connection form 21 26
Connection, affine 28
Connection, Clifford 117 329
Connection, invariant 26 210
Connection, Levi — Civita 33
Connection, on a principal bundle 21
Connection, torsion-free 28
Contraction 18 69
Covariant derivative 22
Covariant derivative, holomorphic 136
Covariant derivative, tensor product 25
Curvature 21 23 44 321
Curvature, cut-off function 84
Curvature, equivariant 210
Curvature, Ricci 34 130
Curvature, Riemannian 33
Curvature, scalar 34 126 134
Curvature, twisting 120
Curvature, twisting equivariant 250
De Rham cohomology 18 128 296
de Rham cohomology, compact supports 19
de Rham's theorem 128
Delta distribution 192
density 30
Density, half 68
Density, integral of 30
Density, Riemannian 34
Density, vertical 278
Determinant line bundle 41 306 348
Determinant line bundle, -metric 306
Determinant line bundle, connection 309 350
Determinant line bundle, curvature 348
Determinant line bundle, Quillen metric 306
Determinant, zeta-function 302
Difference bundle 295
Differential form 17
Differential form, basic 20
Differential form, equivariant 208
Differential form, harmonic 128
Differential form, horizontal 20
Differential form, integral along the fibre 31
Differential form, self-dual 132
Differential form, volume 31
Differential operator 64
Differential operator, elliptic 65
Dirac operator 116
Dirac operator, classical 127 134
Dirac operator, index of 123
Dirac, P.A.M. 102
Divergence 68
Dolbeault cohomology 139
Dolbeault's theorem 139
Duhamel's formula 98 169
Duistermaat — Heckman theorem 226
Duistermaat, J.J. 226
Equivariant -genus 213 249
Equivariant, bundle 16 209
Equivariant, characteristic class 212
Equivariant, Chern character 212
Equivariant, Chern character, relative 192 250
Equivariant, Chern — Weil homomorphism 236 294 352
Equivariant, Clifford module 186
Equivariant, cohomology 209
Equivariant, curvature 210
Equivariant, differential form 208
Equivariant, Euler class 213 218
Equivariant, exterior differential 208
Equivariant, index 186 250 293
Equivariant, relative Chern character 250
Equivariant, superconnection 210
Equivariant, twisting curvature 250
Euler class 58
Euler class, equivariant 213 218
Euler number 59 129 149
Euler number, holomorphic vector bundle 139 152
Exponential map 35
Exponential map, Jacobian of 38 168
Exterior algebra 103
Exterior differential 17 29
| Exterior differential, equivariant 208
Family 278
Family index theorem 338
Family of smoothing operators 314
Flag manifold 232 254
Fourier transform of orbit 224
Frame bundle 16
Frame bundle, orthonormal 32
Freed, D.A. 348
Fundamental one-form 28
Gauss — Bonnet — Chern theorem 59
Gaussian integral 54 72 173 178 223
Generalized section 74
Geodesic 35
Gilkey, P.B. 147 193
Gradient 34
Green operator 92 288
Hamiltonian vector field 214 227
Harish — Chandra 231
Harmonic form 128
harmonic oscillator 145 153
Harmonic spinor 134
Heat equation 75
Heat equation, formal solution 83
Heat kernel 72 75 310
Heat kernel, asymptotic expansion 87
Heckman, G. 226
Hilbert — Schmidt operator 87
Hlrzebruch, F. 150 152 245
Hodge star 131
Hodge's theorem 128 139
Holomorphic vector bundle 136
Horizontal bundle 21
Horizontal lift 21
INDEX 123 145
Index bundle 270 281 299
Index density 146
Index density, equivariant 196
Index density, family 338
Index theorem, equivariant 196 250
Index theorem, local 146 181
Index, equivariant 186 250 293
Index, family see “Index bundle”
Injectivity radius 35
Jacobian of exponential map 38
K-theory 295
Kaehler manifold 137 150 257
Karamata, J. 94
Kernel 74
Kirillov character formula 253
Kirillov formula 249 295 351
Kirillov, A.A. 253
Kodaira vanishing theorem 141
Kostant, B. 255
Kuenneth theorem 129
L-genus 149
Laplace — Beltrami operator 128 133
Laplacian, generalized 65
Leibniz's rule 17 22 44 282
Levi — Civita connection 33
Licbnerowicz formula 126 135 166 334
Lichnecowicz, A. 134
Lie bracket 17
Lie derivative 16
Lie derivative, E. Cartan's homotopy formula 18
Lie superalgebra 39
Liouville form 226 231
Local index theorem 146 181
Local index theorem, equivariant 196 250
Local index theorem, family 338
Localization theorem 215 251
Manifold, almost-complex 135
Manifold, complex 135
Manifold, Hermitian 135
Manifold, Kaehler 137 150
Manifold, Riemannian 32
Manifold, spin 114 144
Manifold, symplectic 214
Mathai, V. 52 241
McKean — Singer formula 124 145
McKean — Singer formula, equivariant 186
McKean — Singer formula, family 299
McKean, H. 124
Mean curvature 321
Mehler's formula 145 154 265 344
Mellin transform 300
Minakshisundaram, S. 101
moment 211
Moment, Riemannian 213 249
Moment, symplectic 214
Moment, twisting 250
Normal coordinates 35 71
Orientation 31
Parallel transport 26
Parametrix 77
Patodi, V.K. 147
Pfaffian 42 224
Pleijel, A. 101
Poincare duality 132
Poincare lemma 52
Poincare — Hopf theorem 59 61 225
Polarization 109
Principal bundle 15
Principal bundle, geodesic distance 198
Principal bundle, heat kernel 175 200
Quantization map 104
Quillen metric 306 348
Quillen, D. 43 46 52 241 306
Radial vector field 35
Relative Chern character 146
Relative Chern character, equivariant 250
Relative Chern character, localized 195
Relative supertrace 113 147
Renormalized limit 302
Ricci curvature 34 130
Riemann — Roch theorem 152 245
Riemann — Roch — Hirzebruch theorem 152
Riemannian curvature 33
Riemannian manifold 32
Riemannian metric 32
Riemannian moment 213 249
Rossman, W. 234
Scalar curvature 34 134
Schwartz kernel theorem 74
Second fundamental form 320
Section 14
Section generalized 74
Segal, G.B. 196
Signature 133 150
Signature operator 133
Signature theorem 150
simplex 77
Singer, I.M. 124 147 150 196 295 339
Smoothing operator 74
Smoothing operator, family 314
Spin group 106
Spin structure 114
Spinor bundle 115
Spinor module 109
Spinor supertrace 110
Stationary phase 226
Superalgebra 38
Superalgebra, Lie 39
Superalgebra, supercommutative 39
Superbundle 39
Supercommutator 39
Superconnection 44 282
Superconnection, Bismut 318
Superconnection, Clifford 117
Superconnection, curvature 44
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