Thomas C.B. — Elliptic Cohomolgy (The University Series in Mathematics) :: Электронная библиотека попечительского совета мехмата МГУ

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Thomas C.B. — Elliptic Cohomolgy (The University Series in Mathematics)

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Название: Elliptic Cohomolgy (The University Series in Mathematics)

Автор: Thomas C.B.

Аннотация:

Elliptic Cohomology is one of few books to present a systematic exposition of the geometric and arithmetic aspects of this extremely beautiful theory: a quotient-oriented cobordism localized away from the prime 2, whose coefficients coincide with a ring of modular forms. Charles B. Thomas constructs this cohomology theory and evaluates it on classifying spaces BG of finite groups G. Elliptic Cohomology is an important resource for mathematicians interested in topology, number theory, geometry, and theoretical and mathematical physics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 199

Добавлена в каталог: 10.06.2008

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Предметный указатель

(Hopkins)      156
Abelian varieties      164
Abelian varieties, dimension 2      167
Abelian varieties, Jacobian      165
Abelian varieties, principally polarized      165
Atiyah invariant      149
Baas — Sullivan construction      27
Baas — Sullivan construction, manifolds with singularity      28
Brown — Peterson theory (BP)      26 87 100
Brown — Peterson theory (BP), -periodicity      27
Burnside ring      44 81 116
Cayley numbers      147 160 183—185
Character ring      36
Character ring, elliptic      117
Characteristic class      8
Characteristic class, Chern      8 62
Characteristic class, generalized      25
Characteristic class, Pontrjagin      9
Characteristic class, Stiefel — Whitney      75
Characteristic class, transferred Euler      92
Characteristic number      9 151 179
Class functions      36
Class functions for pair $\Gamma$ , $\mathbb{F}$       37
Class functions for pair $\mathbb{Z}^n_p$ , $\mathbb{Q}_p$       39
Cobordism ring      7 23 179
Cobordism ring, $\tilde{Spin}$ , $\Omega_{(8)}*$       147 159
Cobordism ring, equivariant       103 113
Cobordism ring, oriented $\Omega_{SO}*$       7
Cobordism ring, Spin, $\Omega_{Spin}*$       23 147
Cohomology of BG      61
Cohomology of BG, Chem subring      62 89
Cohomology of BG, generalized      82
Cohomology of BG, invariant elements      63
Cohomology of BG, p-periodicity      64
Cohomology of BG, p-rank = 2      71 92
Cohomology of BG, spectral sequence of extension      65
Cohomology of BG, stable elements      63
Cohomology, complex oriented      25—26
Cohomology, elliptic      29
Cohomology, elliptic, level 1      100 144
Cohomology, elliptic, level 2      29
Cohomology, elliptic, level N (Baker)      144 146
Cohomology, elliptic, level N (Brylinski)      146
Cohomology, K3/string      159 170—171 176
Completion Theorem      36 110 115
Completion, I-adic      36 42 109 110
Completion, p-adic      36 109
Congruence subgroup $\Gamma(N)$       25 52 187
Contraction property (Segal)      122
Curvature, Ricci (positive)      162
Curvature, scalar (positive)      151 162
Discriminant $\Delta$       24 29 31 144 157
Elliptic curve, Jacobi      12 19 24
Elliptic curve, Weierstrass      24 31
Elliptic homology (Kreck — Stolz) at odd primes      147 151
Elliptic homology (Kreck — Stolz), 2-local      153
Elliptic object      123
Elliptic system (for finite group G)      126
Equivariant elliptic cohomology, $\mathscr{E}ll_G*$ (Devoto)      103
Euler characteristic (equivariant)      81—82
Exceptional Jordan algebra      184
Fermat hypersurface      173
Finite groups, $C_{O_0}$       75
Finite groups, $C_{o_2}$       75
Finite groups, $C_{p^l}$       36 43 62 109
Finite groups,       87
Finite groups, $p_+^{1+2}      $64
Finite groups, $Q_{2'}$       71
Finite groups, $SD_{2'}$       71
Finite groups,       61 87
Finite groups, M      75 141
Finite groups, Mathieu      49 see
Finite groups, order =       98
Finite groups, p-rank = 2      92 97
Flat bundles      35 62 134
Flat bundles, maps      35 42 107 116
Formal group      10 26
Formal group, coordinates      171

Formal group, elliptic curve      24
Formal group, height      40
Formal group, K3-surface (Brauer)      171
Formal group, logarithm      10
Genus zero condition      130
Genus, $\hat{A}$       12
Genus, elliptic      12 161
Genus, L      12
Genus, Mathieu      56
Genus, Ochanine      149
Genus, strongly multiplicative (rigid)      14
Genus, Witten      161
Green functor, associated modules      81
Green functor, axioms      80
Green functor, Frobenius reciprocity      80
Gysin map      26
Hecke algebra      52
Human Capital and Mobility (HCM)      4
Igusa polynomial      109
Isom $(\mathbb{O}P^2)(=F_4)$       184
Johnson — Wilson theory E(n)      91 181
Kriz counterexample      99
Kummer varieties      168
Kummer varieties in dimension 2      169—170
Kummer varieties, defining equations      168 176—177
Kummer varieties, symplectic automorphism group      188
Landweber exactness condition      27 30 181
Loop space, (double)      125 133
Loop space, LBG      123
Loop space, LX      131
Mackey functor, axioms      80
Mackey functor, double-coset formula      80
Mathieu groups, $M_{11}$       49 74
Mathieu groups, $M_{12}$       49 74
Mathieu groups, $M_{21} \approxeq L_3(4)$ , $M_{22}$       50 71—76
Mathieu groups, $M_{21}$       71—73
Mathieu groups, $M_{23}$       49 71—73 137 188
Mathieu groups, $M_{24}$       49 64 68 100 127
Mathieu groups, Coxeter representation      74
Mathieu groups, Steiner systems      49
Mathieu groups, Todd representation $(M_{24})$       51 68
Milnor manifolds $H_{ij}$       15
Mirror Symmetry      177
Modular forms      25 52 173
Modular forms, cusp      52
Modular forms, degree      174
Modular forms, eigenforms      54
Modular forms, generating families      25 144 175
Modular forms, invariance subgroup      52
Modular forms, level      52 56 143 146
Modular forms, topological      157
Modular forms, weight      52
Modular functions      130
Moonshine for $M_{24}$       51 53 130—131
Moonshine for M      141—142
Moonshine, Norton condition      104 142
Morava K-theory K(n)      90 99 101 182
Multiplicative genus      9
Multiplicative sequence      10
Prize question (Hirzebruch)      158
Projective plane functors , $\pi E_*^K$       147
Quantum field theory      119—120
Quantum field theory, conformal      120
Quantum field theory, topological      119
Ramanujan numbers      58
Spectrum      100 153—156 180
Stable cohomotopy      81 116
Theorem, Adams      44
Theorem, Hopkins — Kuhn — Ravenel      42
Theorem, Landweber — Ravenel — Stong      29
Theorem, Lubin — Tate      40
Theorem, Taubes      15
Thompson series      53 55 58 130
Vector bundles with connection      123
Vector bundles, admissible (over LX)      134
Vector bundles, Fock      141
Vector bundles, Virasoro      131 137
Virasoro algebra      132

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