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Spanier E.H. — Algebraic Topology
Spanier E.H. — Algebraic Topology

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Название: Algebraic Topology

Автор: Spanier E.H.

Аннотация:

Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, and topological manifolds. The remaining third of the book is devoted to Homotropy theory, covering basic facts about homotropy groups, applications to obstruction theory, and computations of homotropy groups of spheres. In the later parts, the main emphasis is on the application to geometry of the algebraic tools developed earlier.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 542

Добавлена в каталог: 16.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$G$ structure      90
$H$ cogroup      39
$k$-stem      459
$n$-characteristie cohomology class      425 441
$n$-circuit      148
$n$-connected pair      373
$n$-connected space      51
$n$-duality map      462
$n$-equivalence      404
$n$-factorization      440
$n$-plane bundle      90
$n$-plane bundle, over complex field      90
$n$-simple pair      385
$n$-simple space      384
$n$-sphere bundle      91
$n$-universal element      408
$p$th-power cohomology operation      270
$\check{C}$ech cohomology      327 358—359
$\check{C}$ech cohomology, K$\ddot{u}$nneth formula      359—360
$\check{C}$ech cohomology, universal-coefficient formula      335—336
$\mathcal{C}$-acyclic pair      506
$\mathcal{C}$-acyclic space      506
$\mathcal{C}$-epimorphism      505
$\mathcal{C}$-exact sequence      519
$\mathcal{C}$-isomorphic abelian groups      505
$\mathcal{C}$-isomorphism      505
$\mathcal{C}$-monomorphism      505
$\omega$-homotopic maps      379
$\omega$-homotopy      379
Abelian $H$ cogroup      40
Abelian $H$ group      35
Absolute $CW$ complex      401
Absolute $n$-circuit      148
Absolute homology group      172 175
Absolute Hurewicz isomorphism theorem      397—398
Absolute Hurewicz isomorphism theorem, generalization of      508—509
Absolute neighborhood retract      56
Absolute neighborhood retract, tautness of      290—291
Absolute retract      56
Action of the fundamental group      382—385 420
Acyclic chain complex      163
Additive cohomology operation      270
Adem relations      276
Adjoint functor      41
Adjunction space      56
Admissible lifting      476
Admissible map      476
Affine variety      10
Affinely independent set      10
Alexander cohomology      308
Alexander cohomology, universal-coefficient formula      336
Alexander cohomology, universal-coefficient formula, for compact supports      337—338
Alexander cohomology, with compact supports      320
Alexander duality theorem      296
Alexander — Spanier cohomology      see Alexander cohomology
Alexander — Whitney diagonal approximation      250
Associated graded module      468
Associative coproduct      266
Associative product      263
Attaching map      146
Augmentation      167 213
Augmentation, of cochain complex      237
Augmentation-preserving chain map      168
Augmented chain complex      167 213
Augmented cochain complex      237
Axiom of compact supports      203
Axioms, of cohomology theory      240—241
Axioms, of cohomology theory, of homology theory      199—200
Back $i$-face      250
Ball      9
Bary center      117
Barycentric coordinate      111
Barycentric subdivision      123—124
Barycentric subdivision, interation of      124
Base of cone      116
Base point      15
Base point, nondegeneracy of      380 419
Base space      62 66 90
Base vertex      110 136
Basis      6 8
Betti number      172 176
Bidegree      466
Bigraded module      466
Bijection      2
Bijective function      2
Binormal space      56
Block dissection      277
Bockstein cohomology homomorphism      240
Bockstein cohomology operation      270
Bockstein homology homomorphism      222
Bockstein homomorphism      280—281
Borsuk Homotopy Extension Theorem      57
Borsuk — Ulam theorem      104 266
Boundary      157
Boundary operator      156
Boundary, of homology manifold      277
Boundary, of pseudomanifold      150
Bounded subset      319
Brouwer degree theorem      398
Brouwer fixed-point theorem      151 194
Brouwer theorem on invariance of domain      199
Brown representability theorem      411
Bundle projection      90
Canonical free resolution      219
Canonical map      152
Canonical projection      152
Cap product      254—255
Carrier      112
Cartan formula      271
Category      14
Category, of a topological space      279
Category, of chain complexes      158
Category, of connected covering spaces      79
Category, of contiguity classes      130
Category, of fibrations      69—70
Category, of maps      414
Category, of morphisms      16
Category, of pairs      16
Category, of simplicial pairs      10
Category, opposite      17
Category, small      14
Category, with models      164
Cellular homotopy      403—404
Cellular map      403
Cellular-approximation theorem      404
Chain      157
Chain complex      157
Chain complex, acyclicity of      163
Chain complex, chain contractibility of      163
Chain complex, modulo $\mathcal{C}$      519
Chain complex, over a ring      213
Chain contraction      163
Chain equivalence      163 192
Chain homotopy      162
Chain homotopy class      205
Chain map      158
Chain transformation      158
Characteristic class      261 281
Characteristic map      91 457
Characteristic map, for a cell      146
Classification theorems      427 431 451 452 460
Classifying space      408
Closed edge path      135
Closed path      46
Closed simplex      111
Clutching function      102 455
Coboundary      236
Coboundary operator      236
Cobounded subset      319
Cochain complex      236
Cochain homotopy      236
Cochain map      236
Cocycle      236
Coexact sequence      366 418
Cofibered sum      99
Cofibration      29 33 57
Cofibration, induced      99 (see also Homotopy extension property)
Coherent topology      5
Coherent topology, for simplicial complex      111
Cohomology algebra      264
Cohomology algebra, of projective space      264—265
Cohomology extension of fiber      256
Cohomology functor      407
Cohomology module      236
Cohomology module, with coefficients      237
Cohomology operation      269 429—430
Cohomology operation, additivity of      270
Cohomology operation, induced by coefficient homomorphism      270
Cohomology operation, of Bockstein      270
Cohomology operation, suspension of      431
Cohomology theory      240
Cohomology, K$\ddot{u}$nneth formula      247—249
Cohomology, of a group      502—503
Cohomology, universal-coefficient formula      243 246 283
Cohomology, with local coefficients      282—283
Cohomotopy group      421 461
Collaring      297
Comb space      26
Commutative coproduct      266
Commutative diagram      16
Commutative product      263
Compact pair      203
Compact supports      203
Compact-open topology      5
Compactiy generated space      5
Compatible family, in a presheaf      324
Compatible family, of cohomology classes      261
Compatible family, of homology classes      299
Compatible family, of orientations      207
Complementary degree      468
Completion of presheaf      325
Component, of groupoid      45
Component, of simplicial complex      138
Composite, of functions      2
Composite, of morphisms      14
Comultiplication      39
Comultiplication, homotopy associativity of      39
Comultiplication, homotopy identity for      39
Comultiplication, homotopy inverse of      40
Cone      56 116
Conjugacy class      15
Connected groupoid      45
Connected Hopf algebra      267
Connected simplicial complex      138
Connecting homomorphism      182 213 222 236 240
Constant presheaf      323
Contiguity category      130
Contiguity class      130
Contiguous simplicial maps      130
Continuity property      319 358
Contractible space      25 56
Contraction      25
Contravariant functor      18
Convergent factorization      438
Convergent filtration      468 493
Convergent sequence of fibrations      438
Convergent spectral sequence      467
Convex body      10
Convex set      10
Coordinate neighborhood      292
Coproduct      266
Counit      266
Covariant functor      18
Covering projection      62
Covering projection, induced      98
Covering space      62 103
Covering space, of projective space      80
Covering space, of sphere      80 103
Covering space, of topological group      104
Covering transformation      85
Cross product      231—232 234—235
Cross product, in cohomology      249—250
Crosscap      148—149
cube      9
Cup product      251—253
CW$ approximation      412 420
CW$ complex      401 420
CYCLE      157
Cyclic module      9
Deformable subspace      29
Deformation      29
Deformation retract      30
Deformation retraction      30
Degree      157
Degree, of homomorphism      157
Degree, of map      54 196 207
DG$ group      157
Diagonal approximation      250
Diagonal approximation, of Alexander — Whitney      250
Diagram chasing      186
Diagram, commutativity of      16
Diagram, homotopy commutativity of      25
Difference between two liftings      434
Differential      156
Differential graded group      157
Differential group      156
Dimension axiom      200
Dimension axiom, for cohomology      240
Dimension, of CW complex      401
Dimension, of simplex      108
Dimension, of simplicial complex      109
Dimension, of topological space      152
Dimension, theory of      152
Direct limit      3
Direct limit, of chain complexes      162
Direct limit, of direct system      18
Direct system      3
Direct system, in a category      18
Directed set      3
Discontinuous group      87
Dissection      276—277
Dominated space      421
Double suspension      516—517
Duality in suspension category      463
Duality map      462
Duality theorems, for manifolds      296 351 357
Duality theorems, in suspension category      463
Duality theorems, of Alexander      296
Duality theorems, of Lefschetz      278 297—298
Duality theorems, of Poincar$\acute{e}$      296—297
Duality theorems, of Whitney      281 355
EDGE      134
Edge path      134
Edge path group      136 151 208
Edge path group, of graph      140—141
Edge path groupoid      136
Edge, end of      134
Edge, origin of      134
Eilenberg — MacLane space      424
Eilenberg — Zilber theorem      232—234
Endomorphism, trace of      9
Epimorphism      6
Equalizer      406
EQUIVALENCE      15
Equivalence class      2
Equivalence relation      2
Equivalence, in homotopy      25
Equivalence, naturality of      22
Equivalence, of edge paths      135
Equivalence, of fiber bundles      92
1 2 3 4
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