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Higson N., Roe J. — Analytic K-Homology
Higson N., Roe J. — Analytic K-Homology



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Название: Analytic K-Homology

Авторы: Higson N., Roe J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 424

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^*$-algebra      8
$C^*$-algebra, abstract      16
$C^*$-algebra, Real      387
$C^*$-identity      2
$C^*(G)$, full group $C^*$-algebra      72
$C^*(G)$, reduced group $C^*$-algebra      8
$C^*(T)$, T an operator      2
$C^*(X)$, X a coarse space      149
$C^*_G(X)$      363
$C^*_G(Y, X)$      370
$D^*(X)$      352
$KK^P (A)$, Kasparov K-homology group      205
$K^P(A)$, analytic K-homology      128 215
$K^P(A, A/J)$, relative K-homology group      131 216
$K_0(A)$, K-theory group      86
$K_0(A, A/J)$, relative K-group      92
$K_0(J)$, J non-unital      90
$K_1 (A)$, in terms of unitaries      106
$K_p(A)$, higher K-group      98
$K_p(M)$, K-homology group of a space      305
$M_n(A)$, algebra of $n \times n$ matrices over A      9
$Spin^c$-structure      315
$Spin^c$-structure, on boundary      316
$V_g$, model index one Predholm module      251
$X^b$      219
$\approx$      63
$\lessapprox$      65
$\lesssim$      63
$\lozenge$, Schrbdinger pairing      226 229
$\mathfrak{B}(H)$, algebra of bounded operators      1
$\mathfrak{D}(A)$      123
$\mathfrak{K}(H)$, algebra of compact operators      8 29
$\mathfrak{Q}(H)$, Calkin algebra      29
$\thicksim$, equivalence modulo compacts      63
$\widetilde{K}^n(A)$, reduced analytic K-homology      125
$^o{K}^n(A)$      190
*-homomorphism      3
Adjoint of bounded operator      1
Adjoint of unbounded operator      20
Admissible      see “Projective resolution admissible”
aligned      240 243 291 293
Amenable      61 164 267 374
ample      124 149 173 184 199 213
Ample, very      358
Approximate unit      18 41 48 115
Approximate unit, quasicentral      57—60 66 76 273
Aspherical      289 349 350 357 365
Assembly map      347 364 389
Assembly map, classical      364—366
Assembly map, coarse      354 355 357
Atiyah — Singer index theorem      vii 48 239 305—341 349
Atiyah — Singer Index Theorem, for hypersurfaces      324
Atkinson's Theorem      30 54 240
B(X), algebra of Borel functions      15
Baum — Connes conjecture      x 366—373
Baum — Connes conjecture, coarse      357
Bergman space      51 139 197 333
Block-diagonal      66
Bott generator      94 108 323
Bott Periodicity Theorem      46 54 110—113 118 178 253—258 388
Bott Periodicity Theorem, Cuntz's proof      118—120 197
Boundary map      99 259—264 301 317 354 369
Boundary map, explicit formulae      109 113 218
Boundary map, uniqueness of      261
Bounded set (in coarse geometry)      142
Brown — Douglas — Fillmore Theorem      vii 37 167—188
Busby invariant      54
C(X), $C_0(X)$, algebras of continuous functions      8
Calkin algebra      29 40 92 108 196
Cap product      267
CAR algebra      52 82 90 198
Cartan — Hadamard theorem      144 350
Cauchy's integral formula      301
Cayley transform      21 108
Chern character      186 325 366
Clifford algebra      312 378
Clifford multiplication      306 312
Closable operator      20 272
Close (in coarse geometry)      141 142
Cluster axiom      180 183—185
Coarse map      144
Coarse structure      142 233 352
Coarse structure, associated $C^*$-algebra      149 285
Coarse structure, comparison of      145 289
Coarse structure, metric      143 152—157
Coarse structure, proper      143
Coarse structure, separable      144
Coarse structure, topological      143 157—160
Coarsely equivalent      144
Cobordism invariance      343
Cohen Factorization Theorem      12 25
Cohomology      325 366 373
Cohomology, for planar sets      186
Commutator      34 60 135 243
Commutator, graded      378
Compact operator      8 29
Compact perturbation      204
Compactification      24 143 351
Compactification, coarse      288 329
complete      274
Completely positive      55 79
Concordance      315
Cone      97 260
Contractible      97
Contractive      208 219
Controlled operator      148 285
Controlled Riemannian metric      329
Controlled set      142
Covering isometry      126 149 357
covers      126 149
Covers, uniformly      357
Cuntz algebra      53 82 115 198
Cup product      105
Cyclic      13 15
de Rham operator      307
Degree      378
Denning function      333
Derives      60 76 243
Diagonal operator      33
Difference bundle construction      94
Differential operator      269
Dirac bundle      306
Dirac class      253 254
Dirac connection      309
Dirac operator      306
Dirac operator, on the line      314
Dirac — Toeplitz operator      331
Direct product      183
Direct sum      7 183
Dolbeault operator      308 326
Domain      19
Domain, of an unbounded operator, invariant      278 297
Dual algebra      123
Dual algebra, relative      130
Dual algebra, unreduced      128
Eilenberg swindle      102 116 154 206 360
Elliptic operator      279
Elliptic operator, homology class of      288 294
Elliptic regularity      283
Endomorphism carried by an ideal      384
Energy estimate      275
Exact $C^*$-algebra      82
Excision map      93 216
Excision Theorem and mapping cone      98
Excision Theorem for K-homology      133—137 216
Excision Theorem for K-theory      92—96 114
Ext (A)      41
Ext (X)      36
Extension      36 38 125
Extension, isomorphic      39
Extension, local, of a differential operator      299
Extension, of an unbounded operator      20 300
External product on K-homology      see “Kasparov product”
External product on K-theory      103—105
Faithful representation      12
Fiasque      164
Finite-rank operator      8 280
Five lemma      171
Formal adjoint      271
Formal periodicity      207 234
Fredholm index      29 93 108—110 200 305
Fredholm module      viii-ix 199
Fredholm module, balanced      210
Fredholm module, degenerate      205
Fredholm module, graded      200
Fredholm module, involutive      209
Fredholm module, multigraded      203
Fredholm module, non-degenerate      209
Fredholm module, relative      215
Fredholm module, selfadjoint      208
Fredholm module, summable      235
Fredholm module, unbounded      301
Fredholm module, unital      209
Fredholm operator      29 93
Fredholm operator, graded      240
Free group      62 82 115 201 235 267
Free resolution      190
Friedrichs' mollifier      273 297
Functional calculus      5 22
Functional calculus, Borel      15 135 151
Functoriality of coarse K-theory      151
Functoriality of index pairing      174 325
Fundamental K-homology class      315
Garding's inequality      280—282
Gelfand transform      3
Gelfand — Naimark theorem      10 16
Gelfand — Naimark — Segal construction      12 56
Generalized homology theory      168
Glimm's Lemma      68 69
Graded, algebra      377
Graded, Hilbert space      377
Graded, vector space      377
Grading operator      377
Graph norm      21
Graph of an operator      20
Group $C^*$-algebra, full      72 374
Group $C^*$-algebra, reduced      8 61 201 347 363—373
Group von Neumann algebra      236
Half-exact      96 98 119 176 259
Hardy space      34
Hawaiian earring      180
Hermitian metric      308
Hermitian module      225 381
Hermitian module, graded      384
Higher signature      366
Hilbert transform      54
Hilbert — Schmidt operator      50 74
Homogeneous element (of a graded algebra)      378
Homological algebra      188 190 372
Homotopic      86 249
Homotopic, homomorphisms      97
Homotopic, stably      86 207
Homotopy equivalence      97
Homotopy invariance of K-homology      160—162 249—252
Homotopy invariance of K-theory      97
Homotopy, uniform      359
Hyperbolic group      363
Ideal      17
Ideal supported near a coarse subspace      155
INDEX function      37
Index pairing      173 174
Index, analytic      321
Index, coarse      354
Index, topological      324 328 340
Induced homomorphism      127
Inner automorphism      101
Inner product      1 12
Inner product module      381
Internal product      see “Cap product” “Cup
Inverse limit      182
Isometry      2 101
K-homology      125—133 204—215 305
K-homology, reduced      125
K-homology, relative      131 215—219
K-homology, unreduced      128
K-theory      85—113
K-theory, Kasparov's definition      116
K-theory, of planar sets      186—187
Kadison — Kaplansky conjecture      235
Kahler metric      336
Kasparov group      205
Kasparov product      viii 239 247 249 252 253 259
Kasparov product and elliptic operators      290—293 296
Kasparov product, definition of      243—248
Kasparov product, equivariant generalization of      326
Kasparov product, in KK-theory      268
Kasparov's lemma      135 287 289
Kasparov's Technical Theorem      76—77 135 239 245
Kazhdan projection      73 374
KK-theory, x      237 267 389
Lichnerowicz' theorem      349
Liftable      58 62
Lifting, completely positive      56 58 62 130
Lifting, multiplicative      42
Locally compact operator      130 147 255
Long Exact Sequence      99 129 168
Mapping cone      98
Maximal domain      20 272
Mayer — Vietoris sequence      117—118 157 168 363 371
Milnor — Wolf Theorem      163
Minimal domain      20 272
Multigraded operator      380
Multigrading      203 311 379
Murray — von Neumann equivalent      88 123
Near (in coarse geometry)      154 163
Non-degenerate representation      12 26
Norm topology      6
normal      2
Normal, essentially      36
Normalization of KK(A)      209 255
Normalized loop of projections      100
Normalizing function      286
Novikov conjecture      365—366 369
Nuclear $C^*$-algebra      60 82
Operator homotopy      204
Operator norm      1
Opposite grading      377
Over Fredholm module over a representation      200
Over projection over an algebra      86
Over unitary over an algebra      106
Partial isometry      2 88 230
Partially bounded from below      330
Partition of unity      244
Partition of unity, adapted      245
Partitioned space      233
Path-lifting property      95
Perturbation series      27 293
Poincare duality      343
Point-norm topology      57 97
Poisson summation formula      367
Ponzi scheme      164
Positive element of a $C^*$-algebra      16 24
Positive modulo an ideal      212 239
Positive operator      6—7
Projection      2 85
Projective module      89 381
Projective resolution      189
Projective resolution, admissible      189
Propagation      152
Propagation speed      274 284 288
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