Gilkey P.B. — Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem :: Электронная библиотека попечительского совета мехмата МГУ

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Gilkey P.B. — Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

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Название: Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

Автор: Gilkey P.B.

Аннотация:

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.

Язык:

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 349

Добавлена в каталог: 24.11.2004

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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 $\mathbb{Z}_2$ 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 $(\partial)$       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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