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Авторизация |
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Luck W. — Transformation Groups and Algebraic K-Theory |
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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 -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 335
Connected, (G,n)-connected 33
Connected, (homological) -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 -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 -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 -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 -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 -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, -isomorphic pair 265
Isomorphism, -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 -graded objects with bounded morphisms 181
K-groups, K-groups of the category of finitely generated -modules 328
K-groups, K-groups of the category of finitely generated projective -modules 183
Laplace operator 375
Length, length of a -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, -comodule 162
Module, -contramodule 162
Module, -module 163
Module, -module of finite type 173
Module, --bimodule 166
Module, finitely generated -module 169
Module, free -module 167
Module, free -module with equivalence class of bases 251
Module, projective -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, -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 -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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