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Lundell A., Weingram S. — The topology of CW complexes
Lundell A., Weingram S. — The topology of CW complexes

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Название: The topology of CW complexes

Авторы: Lundell A., Weingram S.


Most texts on algebraic topology emphasize homological algebra, with topological considerations limited to a few propositions about the geometry of simplicial complexes. There is much to be gained however, by using the more sophisticated concept of cell (CW) complex. Even for simple computations, this concept ordinarily allows us to bypass much tedious algebra and often gives geometric insight into the homology and homotopy theory of a space. For example, the easiest way to calculate and interpret the homology of CP^n, complex projective n-space, is by means of a cellular decomposition with only n+1 cells. Also, by a suitable construction we can "realize" the singular complex of a space as a CW complex and perhaps thus give a more geometric basis for some arguments involving singular homology theory for general spaces and a more concrete basis for singular homotopy type. As a final example, if we start with the category of simplicial complexes and maps, common topological constructions such as the formation of product spaces, identification spaces, and adjunction spaces lead us often into the category of CW complexes. These topics, among others, are usually not treated thoroughly in a standard text, and the interested student must find them scattered through the literature.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 222

Добавлена в каталог: 10.03.2013

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Предметный указатель
Absolute neighborhood retract [ANR(C)]      206
Absolute retract [AR(C)]      206
Abstract simplicial complex      17
Abstract simplicial complex, homology of      175
Adjunction chain module      190
Adjunction complex      37-40
Adjunction of cells      45
Adjunction of CW complexes      61-63
Adjunction space      44
Aspherical carrier theorem      76
Attaching cells      45
Attaching map      45
Augmentation (of cellular chains)      158
Barycentric coordinate functions      17
Barycentric subdivision of a regular CW complex      80
Barycentric subdivision of an ssc      86
Boundary of a closed Euclidean cell      1
Boundary operator      151
c-path      23
Canonical form of an ss operator      87
Carrier of a set      20
Carrier topology      19
Carrier, aspherical      75
Carrier, aspherical of a family of sets      28
Carrier, aspherical of a homotopy      76
Carrier, aspherical of a map      28
Cell algebraic      162
Cell closed      1 6
Cell complex      8
Cell complex connected      22
Cell complex countable      9
Cell complex finite      9
Cell complex locally countable      9
Cell complex locally finite      9
Cell complex normal      9
Cell complex regular      9
Cell complex, adjunction of      37-40
Cell complex, dimension of      9
Cell complex, product of      29-32
Cell complex, quotient of      32-37
Cell complex, subcomplex of      8
Cell Euclidean      1
Cell geometric      162
Cell principal      79
Cell regular      9
Cell structure      6
Cell structure, adjunction of      37
Cell structure, product of      29
Cell structure, quotient of      32
Cell, boundary of      1
Cell, face of      79
Cell, open      2 6
Cellular approximation theorem      72
Cellular chains      151
Cellular chains of a product      171 187
Cellular chains of a quotient      177
Cellular chains of an adjunction      190
Cellular chains, augmentation of      158
Cellular chains, boundary operator for      151
Cellular decomposition      8
Cellular equivalence relation      32
Cellular map      27
Cellular maps of CW complexes      69
Chain module, cellular      151
Chain module, cellular normalized      193
Chain module, cellular of an ssc      191
Characteristic map of a CW complex      41
Characteristic map of an n-cell      6
Characteristic map of an n-simplex (ssc)      86
Closure finite cell complex      9
Coarse topology (on a simplicial complex)      128
Cofibration      4
Collapsing subcomplexes      35
Compact CW complex      44
Compact map      201
Compact space      1
Cone      35 40
Cone of a CW complex      63
Cone reduced      35 40
Covering, domination of a space by      2
Covering, domination of a space by mesh of      69
Covering, domination of a space by numerable      201
Covering, domination of a space by, locally finite      202
Covering, domination of a space by, order of      69
CW complex      41
CW complex, adjunction      61
CW complex, cellular chains of      151
CW complex, cellular homology of      152
CW complex, compact      44
CW complex, connected      52 67
CW complex, local contractibility of      67
CW complex, locally countable      51
CW complex, locally finite      49
CW complex, metrizability of      52
CW complex, normal      49 78
CW complex, paracompactness of      53-56
CW complex, product of      56-59
CW complex, quotient of      59-61
CW complex, regular      78-83
CW complex, relative      48
CW complex, singular homology of      155
CW complex, subcomplex of      43
CW complex, subdivision of      65
Deformation      3
Deformation retract      3 117-119
Degenerate chains      191
Degenerate simplex      84
Degree      165
Disjoint union      2
Domination of a space by a covering      2
Domination of a space by a space      127
Dugundji's theorem      207
Eilenberg-Zilber transformation      184
Equi-locally convex (ELCX)      132
Excision      144-151 154
Extension space [ES(C)]      206
Face of a cell      79
Family of identifications on a cell complex      36
Family of identifications on a CW complex      61
Finite type      142
Full map      201
Geometric realization of an ssc      88-95
Geometric realization of Giever      194
Grassman varieties, cellular decomposition of      13-15
Grassman varieties, cellular decomposition of, homology of      161 188
Homotopic maps      2
Homotopic maps relative to a subspace      3
Homotopy      2
Homotopy equivalence      3
Homotopy extension property      4
Homotopy Extension Theorem      68
Homotopy groups      4
Homotopy inverse      3
Homotopy type      3
Incidence number      162
Invariance of domain      5
Isomorphic cell complexes      27
Join      40
Lens space, cellular decomposition of      15-16
Lens space, cellular decomposition of generalized      16
Lens space, cellular decomposition of, homology of      180
Local contractibility of a CW complex      67
Locally compact map      201
Locally compact space      1
Locally contractible space      67
Manifold      5
Manifold homology of 2-dimensional      180-183
Manifold regular cell structure on      82
Mapping cylinder of a cellular map      39 63
Mapping cylinder of an n-ad      117
n-ad      3
n-ad, homotopy equivalence of      119
n-ad, map of      3
n-ad, mapping clyinder of      117
n-simplex, standard      1
n-simplex, standard, standard semisimplicial      85
n-skeleton of a cell complex      8
n-skeleton of a CW complex      47
Neighborhood extension space [NES(C)]      206
Nerve of a covering      128
Nondegenerate simplex      84
Normal cell complex      9
Normal space      1
Normalized chains      193
One point union (wedge)      148
Orientation of a cell      162
Orientation of a CW complex      162
Orientation of a product      171
Orientation of a quotient      177
Paracompact space      202
Partition of unity      201
Perfectly normal space      204
Projective space, cellular decomposition of      11-13
Projective space, cellular decomposition of, homology of      161-179
Proper map      172
Quotient of a cell complex      32-37
Quotient of a CW complex      59-61
Quotient of a CW complex, homology of      177-179
Quotient of an ssc      97-99
Quotient orientation      177
Regular cell complex      9
Regular cellular map      27
Regular CW complex      78
Relative CW complex      48
Relative star subdivision      105
Relative subdivision      107
Semisimplicial complex (ssc)      84
Semisimplicial complex (ssc), adjunction of      99
Semisimplicial complex (ssc), barycentric subdivision of      86
Semisimplicial complex (ssc), geometric realization of      88
Semisimplicial complex (ssc), product of      95
Semisimplicial complex (ssc), quotient of      97
Semisimplicial complex (ssc), regulated      107
Semisimplicial complex (ssc), simplicial subdivision of      99
Semisimplicial complex (ssc), subcomplex of      85
Semisimplicial complex (ssc), triangulation of      100
Semisimplicial map      84
Shrinking lemma      203
Simplex of a set      17
Simplex of an ssc      84
Simplex, standard      1
Simplicial complex      17
Simplicial complex, abstract      17
Simplicial complex, cell structure on      17
Simplicial complex, coarse topology on      128
Simplicial complex, CW topology on      130
Simplicial complex, homology of      171
Simplicial map      18
Simply connected      4
Singular complex      84
Singular simplex of a space      84
Smash product of cell complexes      36 40
Smash product of CW complexes      63
Sphere      2
Sphere, cellular decomposition of      9
Sphere, homology of      174
Sphere, regular cellular decomposition of      10
Star      25
Star refinement      202
Strict equivalence (of cell structures)      7
Subcomplex of a cell complex      8
Subcomplex of a CW complex      43
Subcomplex of a semisimplicial complex      85
Subdivision, barycentric of an ssc      86
Subdivision, barycentric of an ssc of a CW complex      65
Subdivision, barycentric of an ssc, star      105
Suspension of a cell complex      35 40
Suspension of a CW complex      63
Suspension, reduced      35 40
Tietze's extension theorem      207
Triangulation of a regular CW complex      80
Type numbers      13
Unit n-disc      1
Unit n-disc, cellular decomposition of      10
Unit n-disc, regular cellular decomposition of      11
Vertex scheme      17
Vertices of an abstract simplicial complex      17
Weak topology      2 41
Wedge (one-point union)      148
Wedge (one-point union), homology of      149
\mathcal{R}-minimal cells      32
\mathcal{R}-orientation      177
\mathcal{R}-\mathcal{R}-compatible maps      34
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