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Luck W. — Transformation Groups and Algebraic K-Theory
Luck W. — Transformation Groups and Algebraic K-Theory

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Название: Transformation Groups and Algebraic K-Theory

Автор: Luck W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 443

Добавлена в каталог: 18.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian category      165
Absolute torsion      249
Additive, additive category      180
Additive, additive invariant      109
Additive, functorial additive invariant      109
Additive, universal additive invariant      109
Additive, universal functorial additive invariant      110
Admissible functor      186
Approximation, approximation of a chain complex      211
Approximation, approximation of a G-CW-complex      35
Approximation, finite approximation      211
Approximation, finite-dimensional approximation      211
Approximation, finitely generated approximation      211
Approximation, free approximation      211
Attaching, attaching cells      8
Attaching, attaching map      7
Attaching, making highly connected by attaching cells      34
Attaching, obtained by attaching cells      34
Base      167
Base, cellular equivalence class of bases      262
Base, preferred equivalence class of bases      251
Bass — Heller — Swan homomorphism      135 205 299
Boundary, boundary homomorphism of a localization square      368 369
Boundary, boundary of a cell      7
Burnside ring      104
Category, abelian category      165
Category, additive category      180
Category, category of $\mathbb{Z}^{n}$-graduate objects with bounded homomorphisms      181
Category, category with cofibrations and weak equivalences      108
Category, component category      99
Category, discrete fundamental category      149
Category, discrete orbit category      151
Category, EI-category      162
Category, finite EI-category      325
Category, free EI-category      325
Category, fundamental category      144
Category, induced discrete category of a topological category      149
Category, orbit category      145
Category, small category      162
Category, topological category      145
cell      7
Cell, closed cell      7
Cell, open cell      7
Cellular, cellular chain complex      152
Cellular, cellular equivalence class of bases      262
Cellular, cellular homology      263
Cellular, cellular homotopy      32
Cellular, cellular map      32
Cellular, cellular push out      60
Chain      325
Chain complex      211
Chain complex, cellular chain complex      152
Chain complex, chain complex of finite type      211
Chain complex, chain complex with preferred equivalence class of bases      251
Chain complex, elementary chain complex      214
Chain complex, finite chain complex      211
Chain complex, finite-dimensional chain complex      211
Chain complex, finitely dominated chain complex      221
Chain complex, finitely generated chain complex      211
Chain complex, free chain complex      211
Chain complex, positive chain complex      211
Chain complex, projective chain complex      211
Chain complex, round chain complex      248
Chain complex, singular chain complex      259
Chain contraction      215
Chain homotopy representation      293
Character Map      105
Characteristic map      7
Classifying space      56
Cobordism      84
Cobordism, h-cobordism      84
Cobordism, isovariant h-cobordism      84
Cofibration      9
Coherent orientation      393 394
Coinduction      350
Collapse, collaps relative A      62
Collapse, elementary collapse      62 255
Compactly generated      6
Completely regular      27
Complex, (relative) G-CW-subcomplex      21
Complex, chain complex      211
Complex, finite G-CW-complex      28
Complex, finite-dimensional G-CW-complex      28
Complex, finitely dominated G-CW-complex      47
Complex, G-CW-complex      6
Complex, G-CW-complex with round structure      361
Complex, relative G-CW-complex      6
Complex, skeletal-finite G-CW-complex      28
Complex, special G-CW-complex      367
Component category      99
Cone, mapping cone      60 213
Congruences, congruences for degrees      403
Congruences, congruences for the Burnside ring      335
Congruences, congruences for the image of $\overline{\omega}$      335
Connected, (G,n)-connected      33
Connected, (homological) $(\mathfrak{F},v)$-connected      33
Connected, homological n-connected      33
Connected, n-connected      32
Covering, discrete universal covering functor      149
Covering, regular covering      136
Covering, universal covering functor      146
Cylinder, mapping cylinder      60 213
De Rham cohomology      375
Deformation, formal deformation      63 255
Degree      394
Degree, map with invertible degrees      395
Dimension, dimension function      392
Dimension, dimension of a cell      7
Dimension, dimension of a chain complex      211
Dimension, dimension of a G-CW-complex      28 35
Dimension, homological dimension      339
Disc, semilinear G-disc      91
Discrete, discrete fundamental category      149
Discrete, discrete orbit category      151
Discrete, discrete universal covering functor      149
Discrete, induced discrete category of a topological category      149
Domination, finite domination      47 221
EI-cateogry      162
EI-cateogry, finite EI-category      325
EI-cateogry, free EI-category      325
Elementary, elementary collapse      62 255
Elementary, elementary expansion      62 255
Equivalence class of bases      251 262
Equivalent, stably equivalent      238 396
Euclidean neighbourhood retract      37
Euler characteristic      100 227 278 360
Euler ring      104
Even, even G-homotopy representation      392
Expansion, elemenary expansion      62 255
Expansion, expansion relative A      62
Ext-module      340
Extension, extension functor      170
Extension, lift-extension      137
Fibration      311
Fibre homotopy      312
Fibre homotopy equivalence      312
Fibre homotopy equivalence, strong fibre homotopy equivalence      312
Fibre homotopy, strong fibre homotopy      312
Fibre transport      314
Fibre transport, total fibre transport      314
Finite, finite $Ob\Gamma$-set      168
Finite, finite approximation      211
Finite, finite chain complex      211
Finite, finite domination      47 211
Finite, finite EI-category      325
Finite, finite G-CW-complex      28
Finite, finite orbit type      32
Finite, finite resolution      220
Finite, skeletal-finite G-CW-complex      28
Finite-dimensional, finite dimensional approximation      211
Finite-dimensional, finite-dimensional chain complex      211
Finite-dimensional, finite-dimensional G-CW-complex      28
Finite-dimensional, finite-dimensional resolution      220
Finitely generated, finitely generated $R\Gamma$-module      169
Finitely generated, finitely generated approximation      211
Finitely generated, finitely generated chain complex      211
Finitely generated, finitely generated resolution      220
Finiteness obstruction      52 211 278 360
Finiteness obstruction, reduced finiteness obstruction      52 212 278 360
Fixed point set      10
FORM      375
Formal deformation      63 255
Free, free $R\Gamma$-module      167
Free, free approximation      211
Free, free chain complex      211
Free, free EI-category      325
Free, free resolution      220
Functor, admissible functor      186
Functor, discrete universal covering functor      149
Functor, extension functor      170
Functor, inclusion functor      170
Functor, restriction functor      170
Functor, splitting functor      170
Functor, universal covering functor      146
Fundamental, discrete fundamental category      149
Fundamental, fundamental category      144
Fundamental, fundamental groupoid      145
Gap conditions, weak gap condition      88
Group ring      163
Groupoid, fundamental groupoid      145
Harmonic form      375
Hausdorff space      6
Hereditary ring      328
Homological dimension      339
Homology, cellular homology      263
Homology, homology theory      33
Homology, singular homology      263
Homology, weak $\mathfrak{F}$-G-homology equivalence      33
Homology, weak homology equivalence      33 212
Homotopy representation      392
Homotopy representation, even homotopy representation      392
Homotopy representation, homotopy representation group      396
Homotopy, cellular homotopy      32
Homotopy, G-fibre homotopy      312
Homotopy, G-fibre homotopy equivalence      312
Homotopy, homotopy lifting property      311
Homotopy, oriented G-homotopy equivalence      396
Homotopy, simple G-homotopy equivalence      63
Homotopy, simple homotopy equivalence of chain complexes      255
Homotopy, strong G-fibre homotopy equivalence      312
Homotopy, weak $\mathfrak{F}$-G-homotopy equivalence      33
Homotopy, weak G-homotopy equivalence      33
Idempotent completion      182
Inclusion functor      170
Induction      166
Induction over the orbit types      40
Invariant, additive invariant      109
Invariant, functorial additive invariant      109
Invariant, invariant Riemannian metric      375
Invariant, universal additive invariant      109
Invariant, universal functorial additive invariant      110
Irreducible morphism      186
Isomorphic, $\Pi$-isomorphic pair      265
Isomorphism, $\Pi$-isomorphism      265
Isomorphism, isomorphism of (relative) G-CW-complexes      7
Isotropy group, set of isomorphism classes of isotropy objects      173
Isotropy group, set of isotropy groups      32
Isovariant, isovariant G-map      79 84
Isovariant, isovariant h-cobordism      84
Isovariant, isovariant Whitehead group      84
Isovariant, isovariant Whitehead torsion      85
Join      131
K-groups, K-groups of a category with cofibrations and weak equivalences      182
K-groups, K-groups of a G-space      277
K-groups, K-groups of an exact category      182
K-groups, K-groups of the category of $\mathbb{Z}^{n}$-graded objects with bounded morphisms      181
K-groups, K-groups of the category of finitely generated $R\Gamma$-modules      328
K-groups, K-groups of the category of finitely generated projective $R\Gamma$-modules      183
Laplace operator      375
Length, length of a $R\Gamma$-module      325
Length, length of a EI-category      325
Length, length of an object      325
Lift extension      137
Localization square      368
Making highly connected by attaching cells      34
Map, attaching map      7
Map, cellular map      32
Map, character map      105
Map, characteristic map      7
Map, isovariant G-map      84
Map, map with invertible degrees      395
Map, proper map      14
Map, stable map      238
Mapping, mapping cone      60 213
Mapping, mapping cylinder      60 213
Mapping, mapping torus      129
Module, $R\Gamma$-comodule      162
Module, $R\Gamma$-contramodule      162
Module, $R\Gamma$-module      163
Module, $R\Gamma$-module of finite type      173
Module, $R\Gamma_{1}$-$R\Gamma_{2}$-bimodule      166
Module, finitely generated $R\Gamma$-module      169
Module, free $R\Gamma$-module      167
Module, free $R\Gamma$-module with equivalence class of bases      251
Module, projective $R\Gamma$-module      165
Moebius inversion      330
Morphism, irrducible morphism      186
Neighbourhood deformation retract (NDR)      9
Noetherian ring      327
normalizer      11
Obtained by attaching cells      34
Orbit, discrete orbit category      151
Orbit, finite orbit type      32
Orbit, induction over the orbit types      37
Orbit, orbit category      145
Orbit, orbit type      32
Orientation      367 393 394
Orientation, coherent orientation      393 394
Orientation, orientation behaviour      392
Oriented, equivariantly oriented G-manifold      375
Oriented, oriented G-homotopv equivalence      396
Pair, $\Pi$-isomorphic pair      265
Pair, pair of G-CW-complexes      21
Path lifting      27
Picard group      385
Poincare torsion      377
Positive chain complex      211
Projective, projective $R\Gamma$-module      165
Projective, projective chain complex      211
Projective, projective class group      118
Proper, proper G-space      16
Proper, proper map      14
Push out      10
Push out, cellular G-push out      60
Push out, G-push out of spaces with simple structure      76
Rank      199
Reduced, reduced equivariant Reidemeister torsion      363
Reduced, reduced finiteness obstruction      52 212 278 360
Reduced, reduced projective class group      118
Regular, completely regular space      27
Regular, regular covering      136
Regular, regular space      136
Reidemeister torsion, equivariant Reidemeister torsion      362 375 376
Reidemeister torsion, reduced equivariant Reidemeister torsion      363
Relative, relative G-CW-complex      6
Relative, relative G-CW-subcomplex      20
Resolution      220
Resolution, finite resolution      220
Resolution, finite-dimensional resolution      220
Resolution, finitely generated resolution      220
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