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| Rourke C.P., Sanderson B.J. — Introduction to Piecewise-Linear Topology |
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| Предметный указатель |
Abstract isomorphism 20
Abstract polyhedron 26
Abstract simplicial complex 26
Adding handles 80
Adding lemma 80
Alexander duality 100
Alexander trick 37
Ambient isotopy 37
Annulus theorem 36
ARC 1
Attaching cells 101
Attaching map of handle 74
Attaching sphere and tube of handle 74
Ball 8
Ball complex 27
Ball, Joins of 23
Ball, joins of pairs of 52
Ball, pairs of 50
Ball, unknotting pairs of, in codimension  91—92
Ball, unknotting pairs of, in codimension 2 92
Barycentre of simplex 11
Based handle 89
Basepoint 100
Belt sphere and tube of handle 74
Bordism, bibliography 118
Boundary of cell 13
Boundary of cobordism 87
Boundary of cube 4
Boundary of manifold 7
Boundary of simplex 12
Cancellation lemma 78
Cancelling handles 78
cell 13
Cell complex 14
Cell in CW complex 101
Cell is a ball 21
Cell, convex 13 27—30
Cell, pairs of 51
Cellular collapse 104
Cellular expansion 104
Cellular isomorphism 16
Cellular map 16
Cellular moves 54—55 65
Characteristic map for cell 101
Characteristic map for handle 74
Closed manifold 7
Closed map 60
Cobordism 9
Cobordism with boundary 87
Cobordism, bibliography 118
Cobordism, handles on 75
Cobordism, invertible 93
Cocore of handle 74
Codimension 50
Coefficients 100
Cohen’s simplicial neighbourhood theorem 34—35
Cohomology 100
Collapse and collapsing 39 et seq.
Collapse for pairs 54
Collapse, cellular 104
Collapse, collapsing and regular neighbourhoods 40
Collapse, internal 105
Collapse, notes 109—110
Collapse, polyhedral 105
Collar and collaring 24
Collar for pairs 52
Collar theorem 24
Collar, local 24
Collars as regular neighbourhoods 36
Collars, regular neighbourhood collaring theorem 36
Combinatorial annulus theorem 36
Combinatorial manifold, notes 108
Complement, simplicial 32
Complementary handles 78
Complex cell 14
Complex simplicial 16
Complex, ball 27
Complex, dual 27
Computing homology 102
Concordance of embeddings 96
Cone 2
Cone construction 5—6
Cone on complex 15
Cone on p.l. map 6
Cone pair 48
Cone, dual 27
Connected sum 46
Connectivity, simple and higher 101
Constructing h-cobordisms 90
Contractible 98
Convex cells 13 27—30
Convex set 13
Coordinate neighbourhood 7
Core of handle 74
Critical dimension for linking 69
cube 4
CW 101
CW associated to a decomposition 83
CW complex 101
CW, subdivision of 105
CYCLE 98
Decomposition (handle) 81
Decomposition, associated CW complex 83
Decomposition, nice 82
Decomposition, simplifying 84
Decomposition, symmetrical 82
Deformation retract 98
Derived neighbourhood 32
Derived neighbourhood for pairs 52
Derived subdivision 20
Derived, near subcomplex 32
Diagram of maps 18
DIMENSION 12
Disc 8
Disc theorem 44
Disc theorem for pairs 56
Dual complex 27 84
Dual cone 27
Duality theorems 84 100
Elimination of handles 85—86
Embedding in codimension (Irwin’s theorem) 96
Embedding in double dimension (Penrose — Whitehead — Zeeman theorem) 63
Embedding, bibliography 113 116
Embedding, notes 111
Engulfing 94
Engulfing, bibliography 114
Epsilon ( -) homotopy 60
Epsilon (-) isotopy 60
Epsilon (-) neighbourhood 32
Euclidean space 1
Exactness 97
Excision 98
Expansion (cellular) 104
Extending collars 57
External join 22—23
Face of cell 14
Face of cube 4
Face of simplex 11
Five dimensional theorems 93—94
Foundations, bibliography 112
Full subcomplex 31
Fundamental group 101
General position 60—63 64
General position theorem for embeddings 61
General position theorem for maps 61
General position, bibliography 113
Geometric interpretation of homology 98
Geometric topology, notes 108
Gluing 26
h-cobordism 9
| h-cobordism theorem 9
h-cobordism, classification 90
h-cobordism, construction 90
h-cobordism, notes 109
h-cobordism, proof of theorem 87
h-cobordism, relative theorem 87
h-cobordism, weak five dimensional theorem 93
Handle 74 et seq.
Handle decomposition 81
Handle of adjacent index 76
Handle on cobordism 75
Handle, adding 80
Handle, based 89
Handle, bibliography 114
Handle, cancelling 78
Handle, complementary 78
Handle, eliminating 85—86
Handle, incidence number of 77
Handle, introduction 79
Handle, nice decomposition 82
Handle, reordering 76
Handle, terminology 74
Hauptvermutung, bibliography 118
Homeomorphism, p.l. 6
Homeomorphism, periodic 26
Homogeneity of manifolds 44
Homology 97
Homology between cycles 99
Homology linking number 72
Homology of sphere 99
Homology triviality of links 69—70
Homology, bibliography 115
Homology, computation of 102
Homology, geometric interpretation of 98
Homotopy 97
Homotopy equivalence 98
Homotopy groups 100
Homotopy, - 60
Homotopy, simple 39 107
House with two rooms 2 40
House, notes 108
Immersion theory, bibliography 117
Incidence number in  89 103
Incidence number of cell 102
Incidence number of handle 77
Independent set 11
Independent subsets 22
Index of handle 74
Induced orientation for boundary of manifold 45
Interior of cell 13
Interior of manifold 7
Internal collapse 105
Intersection number 68 100
Intersection number in 72
Introducing handles, introduction lemma 79
Invertible cobordism 93
Irwin’s embedding theorem 96
Isomorphism, abstract 20
Isomorphism, cellular 16
Isotopy 37
Isotopy extension 56—59
Isotopy extension theorem 58
Isotopy uniqueness of regular neighbourhoods 38
Isotopy, - 60
Isotopy, ambient 37
Isotopy, bibliography 113
Isotopy, locally trivial 58
Isotopy, notes 110
Isotopy, support of 37
Join 1
Join of balls and spheres 23
Join of maps 23
Join of pairs of balls and spheres 51
Join, bibliography 112
Join, external 22—23
Join, simplicial 23
Lefschetz duality 84 100
Level preserving 37
Level preserving lemma 58
Levine’s unknotting theorem 92
Linear cell 13
Linear map 1
Linear subspace 1
Linear triangulation 18
Link 2
Link of simplex 23
Link of spheres 69
Link of vertex in simplicial complex 20
Link pair 48
Linking number 72
Local collaring 24
Local collaring for pairs 52
Local extension of collar 57
Local flatness 47 50
Local triviality of isotopy 58
Manifold 7
Manifold embedding theorems 63 96
Manifold pair 50 51
Manifold, homogeneity 44
Map, cellular 16
Map, linear 1
Map, p.l. 5
Map, simplicial 16
Mapping cylinder 107
Morse function, notes 109
Naturality 97
Neighbourhood, - 32
Neighbourhood, derived 32
Neighbourhood, regular 33 et seq.
Neighbourhood, simplicial 32
Newman’s theorem (corollary 3.13) 35
Newman’s theorem, notes 109
Nice handle decomposition 82
Non-degenerate map 61
Normal bundles, bibliography 115
Orientation induced on boundary 45
Orientation of manifold 43 et seq.
Orientation, definition independent of algebraic topology 46
Orientation, oriented cycle 98
Orientation, standard orientation for spheres and balls 45
P.l. embedding 7
P.l. homeomorphism 6
P.l. invariant 6
P.l. manifold 7
P.l. map 5
P.l., notes 108
Pairs 50 et seq.
Periodic homeomorphism 26
Piecewise-linear see “P.l.”
Piping 67
Poincare conjecture 8
Poincare duality 84 100
Poincare theorem (dimension  ) 8
Poincare, bibliography 114
Poincare, notes 108—109
Poincare, weak 5-dimensional theorem 94
Polyhedral collapse 105
Polyhedron 2
Polyhedron, abstract 26
Polyhedron, examples 2
Polyhedron, non-examples 2
Polyhedron, notes 108
Polyhedron, pairs of 50
Projection, radial 6
Proper manifold pair 50
Pseudo-radial projection 20—21
Radial projection 6
Realising abstract simplicial complexes 26
Reduction of collar 57
Regular neighbourhood 33 et seq.
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