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Hirzebruch F. — Topological Methods in Algebraic Geometry
Hirzebruch F. — Topological Methods in Algebraic Geometry

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Название: Topological Methods in Algebraic Geometry

Автор: Hirzebruch F.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 234

Добавлена в каталог: 30.06.2008

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Предметный указатель
$A^{p, q}$, $A^{p, q}(W)$      119
$A^{p}$      37
$A_{k}$, $\hat{A}_{k}$      13 197
$B^{p, q}$      123
$B^{p, q}(V, W)$      121
$b_r(V)$      72 124
$C^*$-bundle      49
$C^{\infty}$      24
$C^{\infty}$-differentiable      6 24 89
$L_j$      12
$s(M_n)$      112
$T_K$      13
$T_y$-characteristic of a GL(q, C)-bundle      97
$\Box$      121
$\Delta (q, C)$      50
$\Delta$      123
$\hat{A}$-genus      197 198
$\hat{A}(X)$      197
$\hat{A}(X, \frac{1}{2}, \eta)$      197
$\imath (a, b)$      120
$\mathfrak{A}(W)$      46
$\mathfrak{A}^{p, q}$, $\mathfrak{A}^{p, q}(W)$      118
$\mathfrak{A}^{p}$      36
A(SO(k))      83
A-genus      77
Action of a group      40 195
Adjoint operator      121 186
Admissible chart for complex manifold      25 67
Admissible chart for differentiable manifold      24 66
Admissible chart for fibre bundle      40
Admissible space      57
Agranovic, M.S.      186
Akizuki, Y.      139 140
Algebraic curve      2 4 5 143 156
Algebraic manifold      1
Algebraic surface      5 153 154
Almost complex manifold      67
Almost complex structure      67
Almost complex submanifold      70
Alternating cochains      57
Analytic index      186 196
Analytic sheaf      167
Anti-isomorphism      117
Anti-isomorphism $\sharp$, $\widetilde{\sharp}$      120
Arithmetic $\chi(V)$      2 123
Arithmetic genus $p_{\sigma}(V)$, $P_{\sigma}(V)$      1 151
Associated fibre bundle      41
Associated partition of unity      30
Atiyah, M.F.      1 2 13 14 51 56 73 90 113 158 166 173 176 178 179 182 183 184 187 188 193 194 195 196 198 199 200 201
Automorphic forms      152 161 164 165 201
Axioms for Chern classes      58
Axioms for Whitney classes      73
B (G)      74
B(SO{k))      83
B(U(q)), B(O(k))      74
B(W), B(X)      179 189
B, $\mathfrak{B}$      9
Basis      16
Basis sequence      79
Bergmann metric      161
Bernoulli numbers      12
Bernoulli polynomials      16
Bertini, E.      139
Betti number $b_r(V)$      72 124
Birational invariance      2 176
Blanchard, A.      142 215
Bochner, S.      140 215
Borel, A.      49 58 60 61 65 103 104 112 113 141 156 157 158 162 163 164 169 170 171 172 173 175 180 183 198 199 201 202 205
Bott, R.      51 161 169 182 183 195 196 199 201
Bounded domain      161
Bounded manifold      81 82
Bourbaki, N.      29 46 47
Brieskorn, E.      160 201
Bundle $\xi^{\Delta}$ along the fibres      100 174 205
Calabi, E.      215
Canonical $C^*$-bundle      98
Canonical divisor      2 117
Canonical isomorphisms      47
Canonical line bundle      117
Canonical presheaf of a sheaf      20
Cartan, E.      159 163
Cartan, H.      1 4 5 7 16 34 51 74 114 118 122 167 168 169 188 193
Cassels, J.W.S.      166
Cauchy, A.L.      11 12 14
Cech cohomology      57 62 73
cell      50
ch, $ch(\xi)$      91
Characteristic power series of an m-sequence      9
Chern character of coherent analytic sheaf      172
Chern character of difference bundle      179
Chern character of element of K(X)      177
Chern character of U(q)-bundle      91
Chern classes of a complex manifold      68
Chern classes of an almost complex manifold      67
Chern classes of U(q)-bundle      58
Chern numbers of a manifold      92 112
Chern, S.S.      2 64 85 90 157
Chevalley, C.      103
Chow, W.L.      1 158 172
Class $C^{\infty}$      24
Classification theorem for bundles      58 74
Classifying space      74
Cobordant      82
Cobordism ring      82 89 112 194
Coboundary homomorphism      25 28 29
Cochain      25
Cocycles      38
Cofine coverings      17
Coherent      167
Cohomology class of a line bundle      5 127
Cohomology groups      57
Cohomology groups with coefficients in a presheaf      26
Cohomology groups with coefficients in a sheaf      26
Cohomology set $H^1 (X, \Sigma)$      38
Compact space      17
Complete intersection      159
Complex analytic fibre bundle      41
Complex analytic function      25
Complex analytic split manifold      105
Complex analytic vector bundle      45
Complex cobordism ring      112
Complex harmonic forms      121
Complex Laplace — Beltrami operator $\Box$      121
Complex manifold      24
Complex submanifold      69
Conjugate vector bundle $\overline{W}$      117
Conner, P.E.      90 194
Constant sheaf      23
Continuous action      40
Continuous fibre bundle      41
Continuous vector bundle      45
Covering      17
Covering, locally finite      30
Covering, point finite      30
Covering, proper      17
D, [D], {D}      115
d-homomorphism      133
de Rham, G.      6 24 35 37 123 124 190 208 213
Degree of a line bundle      144
Diagonal $C^*$-bundles      53
Dieudonne, J.      30
Difference bundle      179
Differentiable      6 89
Differentiable fibre bundle      41
Differentiable manifold      24
Differentiable submanifold      68
Differentiable vector bundle      45
Differential forms      35 36
Differential forms of type (p, q)      68 118
Differential operator      121 184 185
Differential p-forms      36
Differentials of first kind      1 124
DIMENSION      8 57
Dirac operator      198
Direct image sheaf      168
Direct limit      19
Distinguished element      38
Divisor classes      115
Divisor D of V      114
Divisor of meromorphic function      115
Dolbeault, P.      4 6 7 114 118 119 127
Dold, A.      51 74 89
Dombrowski, P.      47 186
Drivative of a p-form      36
Dual bundle $\xi^{*}$      48
Dual vector bundle $W^*$      47
Duality formula for $T_y$-characteristic      97 99
Duality formula for Todd genus      93 95
Duality operator *      120
Duality theorem of Serre      122
Dynin, A.S.      186
Eckmann, B.      125 215
Effective action of group      40
Effective harmonic form      125
Eger — Todd classes      2
Eilenberg, S.      19 57 83 178
Element of type(p, q)      118 124
Elliptic differential operator      121 185
Embedding      21 198
Epimorphism of presheaves      19
Epimorphism of sheaves      18
Euler class $e(\xi)$, e(W)      71 180
Euler — Poincare characteristic $E(V_n)$      70 72
Euler — Poincare characteristic $\chi(V, W)$      122
Euler — Poincare characteristic $\chi(X, \Sigma)$      33
Exact cohomology sequence for presheaves      29
Exact cohomology sequence for sheaves      33
Exact sequence      21
Exact sequence of vector bundles      54
Extension of a section      51
Extension of a sheaf      23 174
Exterior product      46
Extraordinary cohomology theory      178 183
Fibre      40
Fibre bundle      8 40
Fibre bundle, complex analytic      41 114
Fibre bundle, continuous      41
Fibre bundle, differentiate      41
Fine resolution      35
Fine sheaf      34
Flag manifold      50 109
Floyd, E.E.      90 194
Formal adjoint of differential operator      185 186
Forms of degree p      35
Forms of the first kind      124
Forms of type (p, q)      68 118
Forms of type (p, q) with coefficients in W      119
Four term formula      131 160
Frenkel, J.      74
Functional equation for virtual $T_{\nu}$-genus      95
Functional equation for virtual $\chi_{\nu}$-characteristic      136
Functional equation for virtual index      88
Fundamental class of Kahler metric      123
Fundamental cycle of oriented manifold      3 76
G-bundle      8 41
G-vector bundle      195
Galois, E.      108
Gelfand, I.M.      186
Generalised Todd genus      93
Genus of a multiplicative sequence      77
Geometric genus      2
Germ      19
Godement, R.      16 74 168 169
Grassmann manifold      50
Grauert, H.      16 139 167 169 170
Griffiths, P.A.      140
Grothendieck group $K'_{\omega}(X)$      171
Grothendieck group $K_{\omega}(X)$      170
Grothendieck ring K(X)      177
Grothendieck — Riemann — Roch theorem      172 201
Grothendieck, A.      42 60 74 75 118 158 166 167 170 172 173
Group of divisor classes      115
Group of divisor classes of a Kahler manifold      127
Group of divisor classes of an algebraic manifold      141
Gugenheim, V.K.A.M.      203
Guggenheimer, H.      125
Gysin homomorphism      63 71 171 183
Harish — Chandra      163 165
Harmonic forms      121
Harmonic forms of type (p, q) and class k      126
Hausdorff space      16
Helgason, S.      162 163
Hermitian anti-isomorphism      118
Hermitian metric on V      123
Hilbert characteristic function      1 151
Hirsch formula      75 163
Hodge index theorem      125—127 158 190
Hodge manifold      139
Hodge, W.V.D.      1 2 6 124 125 127 139 190
Holmann, H.      42 45 51 52 74
Holomorphic divisor      115
Holomorphic forms      118
Holomorphic function      25
Holomorphic map      168
Holomorphic section      41
Holomorphically complete manifold      168
Hom(W, W')      47
Homogeneous bounded domain      161
Homomorphism of presheaves      19
Homomorphism of sheaves      18
Homomorphism of vector bundles      54
Homotopic maps      50
Homotopy operator      26 34
Hope $\sigma$-process      176
Hope manifold      215 217
Horrocks, G.      166
Hyperplane      58 139
Hyperplane sections      139
Hypersurface      159
Image of sheaf homomorphism      21
Imbedding      see “Embedding”
Immersion      198
Index of bilinear form      84
Index of elliptic operator      186 196
Index of Kahler manifold      125
Index of oriented manifold      84
Index theorem of Atiyah — Singer      187 196
Index theorem of Hirzebruch      86 196
Index theorem of Hodge      125 190
Indicator      107
Induced G-bundle      43
Induction method in algebraic geometry      145
Integrality of Todd genus      111 113 184 199
Integrality theorems for almost complex manifolds      113 184
Integrality theorems for differentiate manifolds      197—199
Irregularity      2
Ise, M.      165 217
Isomorphism classes of fibre bundles      8 41
Isomorphism of fibre bundles      40
Isomorphism of presheaves      19
Isomorphism of sheaves      18
Isomorphisme canonique      47
Jacobian matrix      66 67
K-genus      77
Kahler manifold      123
Kahler metric      123
Kahler, E.      2 123
Kahn, P.J.      90
Kaup, L.      169
Kenneth theorem for sheaves      169 174
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