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| Lueck W. — Basic introduction to surgery theory |
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| Предметный указатель |
(weakly) excisive 153
(weakly) homotopy invariant 153
Acyclic, U-acyclic 38
Alexander trick 2
Arf invariant 95
Assembly map 149
Associated contravariant Or(G)-space of a left G-space 145
Attaching maps 9
Based exact sequence 28
Basis, equivalent basis 10
Basis, stable basis 107
Basis, stably U-equivalent 107
Basis, U-equivalent 107
Bernoulli numbers 133
Bordism See cobordism
Boundary of a non-degenerate  -quadratic form 100
Brieskorn variety 141
Cell, closed 9
Cell, open 9
Cellular basis 10
Cellular map 31
Cellular pushout 32
centralizer 165
Chain complex, contractible 28
Chain complex, finite 28
Chain complex, finite based free 28
Chain complex, free 28
Chain complex, projective 28
Chain contraction 28
Characteristic map 9
Classifying map of a principal G-bundle 40
Classifying space for G 40
Classifying space with respect to a family of subgroups 148
Cobordism 1
Cobordism, diffeomorphic relative  1
Cobordism, h-cobordism 2
Cobordism, over 1
Cobordism, trivial 2
Cocompact 25
Collaps map 57
Conjecture, Baum — Connes Conjecture 150
Conjecture, Borel Conjecture 151
Conjecture, Farrell — Jones Isomorphism Conjecture 150
Conjecture, Isomorphism Conjecture 149
Conjecture, Kadison Conjecture 152
Conjecture, Novikov Conjecture 151
Conjecture, Poincare Conjecture 2
Conjecture, Stable Gromov — Lawson — Rosenberg Conjecture 152
Degree 40
Disk bundle 57
Dual chain complex 33
Dual R-module 32
Eilenberg — MacLane space 120
Elementary collaps 34
Elementary expansion 34
Embedding, trivial 7
Euler characteristic 53
Exotic sphere 2
Family of finite subgroups 148
Family of subgroups 148
Family of virtually cyclic subgroups 148
Fibration, orientable 61
Fibration, strong fiber homotopy equivalent 61
Form, -quadratic 89
Form, -symmetric 87
Form, non-degenerate -quadratic 89
Form, non-degenerate -symmetric form 87
Form, stably isomorphic -quadratic formations 99
Form, standard hyperbolic -quadratic form 90
Form, standard hyperbolic -symmetric form 87
Form, trivial -quadratic formation 99
Form, U-based -quadratic forms 108
Formation, -quadratic formation 99
Framing, almost stable 127
Framing, stable 127
Free unitary representation 39
Fundamental class 51
G-CW-complex 146
G-CW-complex, proper 147
Group, virtually cyclic 148
Groups of homotopy spheres 124
Handle 4
Handle, boundary of the core 4
Handle, cocore 4
Handle, core 4
Handle, dual 18
Handle, transverse sphere 4
Handlebody decomposition 4
Handlebody decomposition, dual 17
Homology, (proper) equivariant homology theory 162
Homology, Borel homology 147
Homology, G-homology theory 146
Homology, proper G-homology theory 162
Homology, with coefficients in a spectrum over the orbit category 147
Homotopy n-sphere 123
Hopf construction 132
Induction structure 162
Intersection pairing 54
Intersection pairing for immersions 81
Intersection pairing for kernels 86
Involution of rings 50
Involution, w-twisted involution of a group ring 50
J-homomorphism 132
Join 40
Join, fiberwise join of spherical fibrations 60
k-connected map 70
L-group, decorated quadratic i-groups in even dimensions 109
L-group, decorated quadratic i-groups in odd dimensions 109
L-group, quadratic L-groups in even dimensions 93
L-group, quadratic L-groups in odd dimensions 102
L-group, simple quadratic L-groups 110
Lagrangian 93
Lagrangian, complementary 100
Lagrangian, subLagrangian 93
| Lemma, Cancellation Lemma 6
Lemma, Diffeomorphism Lemma 5
Lemma, Elimination Lemma 7
Lemma, Franz' Independence Lemma 46
Lemma, Homology Lemma 14
Lemma, Isotopy Lemma 5
Lemma, Modification Lemma 15
Lemma, Normal Form Lemma 16
Lens space 39
Mackey functor 164
Mapping cone of a chain map 28
Mapping cone of a map of spaces 36
Mapping cylinder of a chain map 28
Mapping cylinder of a map of spaces 36
Module over a Green functor 166
Module, stably finitely generated free 88
Module, stably U-based 107
Module, U-based 107
Normal bordism 106
Normal bundle 57
Normal invariant, normal k-invariant 64
Normal invariant, set of normal invariants 65
Normal invariant, set of normal k-invariants 65
Normal map 67
Normal map of degree one 67
Normal map of manifolds with boundary 105
Normal map with respect to the tangent bundle 68
Normal map, with respect to the tangent bundle 68
normalizer 165
Orbit category 144
Orientation homomorphism of a Poincare complex 51
Orientation homomorphism of a spherical fibration 61
Orientation of an orientable spherical (k-1)-fibration 61
Poincare  -chain homotopy equivalence 51
Poincare complex finite n-dimensional 51
Poincare complex simple finite n-dimensional 51
Poincare pair finite n-dimensional 54
Poincare pair simple finite n-dimensional 54
Ring with involution 32
Selfintersection element 83
Set of normal maps to a compact manifold 117
Set of normal maps to a Poincare complex 67
Signature, higher 151
Signature, of a finite oriented 4k-dimensional Poincare complex 54
Signature, of a symmetric bilinear non-degenerate pairing 54
SIMPLE 113
Simple homotopy equivalence 34
Smash product 57
Space over a category 144
Spectrum 59 144
Spectrum,  -spectrum 144
Spectrum, covariant -spectrum 144
Spectrum, homotopy groups of see stable homotopy groups of a spectrum
Spectrum, map of spectra 144
Spectrum, over a category 144
Spectrum, weak homotopy equivalence 144
Sphere bundle 57
Spherical fibration 60
Spivak normal fibration 62
Stable homotopy groups 131
Stable homotopy groups of a spectrum 60 144
Stable n-th stem 132
Stably parallelizable 125
Structure set 114
Surgery obstruction for manifolds with boundary 106
Surgery obstruction for manifolds with boundary and simple homotopy equivalences 110
Surgery obstruction in even dimensions 96
Surgery obstruction in odd dimensions 104
Surgery problem 77
Surgery program 3
Surgery sequence 118
Surgery sequence, for the Pi-category and topological category 120
Surgery step 77
Suspension 28
Suspension of a pointed space 57
Suspension of a spherical fibration 60
Tensor product of a  -spectrum with a -space 145
Tensor product of spaces over a category 145
The Surgery Step 75
Theorem, Classification of Homotopy Spheres 123
Theorem, Diffeomorphism Classification of Lens Spaces 45
Theorem, Differentiable Sphere Theorem 142
Theorem, Existence and Uniqueness of the Spivak Normal Fibration 62
Theorem, h-Cobordism Theorem 2
Theorem, Homotopy Classification of Lens Spaces 41
Theorem, Homotopy Theoretic Interpretation of the Kervaire — Milnor Braid 138
Theorem, Immersions and Bundle Monomorphisms 74
Theorem, Kervaire — Milnor Braid 138
Theorem, Normal Maps and G/0 69
Theorem, Pontrjagin — Thom Construction 58
Theorem, Pontrjagin — Thom Construction and Oriented Bordism 59
Theorem, s-Cobordism Theorem 1
Theorem, Simple Surgery Obstruction Theorem for Manifolds with Boundary 111
Theorem, Sphere Theorem 142
Theorem, Surgery Exact Sequence 118
Theorem, Surgery Exact Sequence for PL and TOP 119
Theorem, Surgery Obstruction Theorem for Manifolds with Boundary 106
Theorem, Surgery Obstruction Theorem in Even Dimensions 95
Theorem, Surgery Obstruction Theorem in Odd Dimensions 102
Thom class 61
Thom Isomorphism 61
Thom space of a spherical fibration 60
Thom space of a vector bundle 57
Triad, manifold triad 105
Triad, Poincare triad 105
U-torsion of a contractible finite U-stably based chain complex 108
U-torsion of a stable isomorphism of stably U-based modules 107
Unit disk 39
Unit sphere 39
Universal principal G-bundle 40
Whitehead group 25
Whitehead group of a space 31
Whitehead torsion 31
Whitehead torsion of a chain homotopy equivalence 28
Whitney's Approximation Theorem 74
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