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Rourke C.P., Sanderson B.J. — Introduction to Piecewise-Linear Topology
Rourke C.P., Sanderson B.J. — Introduction to Piecewise-Linear Topology



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Название: Introduction to Piecewise-Linear Topology

Авторы: Rourke C.P., Sanderson B.J.

Язык: en

Рубрика: Математика/Геометрия и топология/Общая топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 123

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\geqq3$      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 $\geqq3$ (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 ($\varepsilon$-) homotopy      60
Epsilon ($\varepsilon$-) isotopy      60
Epsilon ($\varepsilon$-) 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, $\varepsilon$-      60
Homotopy, simple      39 107
House with two rooms      2 40
House, notes      108
Immersion theory, bibliography      117
Incidence number in $\mathbb{Z}\pi$      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 $\mathbb{Z}\pi$      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, $\varepsilon$-      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, $\varepsilon$-      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 $\geqq6$)      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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