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Hatcher A. — Algebraic Topology
Hatcher A. — Algebraic Topology

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Название: Algebraic Topology

Автор: Hatcher A.

Аннотация:

In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.


Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 544

Добавлена в каталог: 20.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$ complex (Delta-complex)      103
$\Omega$-spectrum      396
Abelian space      342 417
Action of $\pi_1$ on $\pi_n$      342 345 421
Action of $\pi_1$ on a covering space fiber      69
Action of a group      71 457
Acyclic space      142
Adams      427
Adem relations      496 501
Adjoint      395 462
Admissible monomial      499
Alexander      131 177
Alexander duality      254
Alexander horned sphere      169 170
Amalgamation      456
Aspherical space      343
Attaching cells      5
Attaching spaces      13 456
Augmented chain complex      110
Barratt — Kahn — Priddy theorem      374
Barycenter      119
Barycentric coordinates      103
Barycentric subdivision      119
Base space      377
Basepoint      26 28
Basepoint-preserving homotopy      36 357 421
Basis      42
Betti number      130
Binomial coefficient      287 491
Bockstein homomorphism      303 488
Borel construction      323 458 503
Borel theorem      285
Borsuk — Ulam theorem      32 38 176
Bott periodicity      384 397
Boundary      106 253
Boundary homomorphism      105 108 116
Brouwer      32 114 126 134 173 177
Brown representability      448
BSO(n)      440
BSU(n)      440
Bundle of groups      330
Burnside problem      80
Cap product      239
Cartan formula      489 490
Category      162
Cayley graph, complex      77
Cech cohomology      257
Cech homology      257
cell      5
Cell complex      5
Cellular approximation theorem      349
Cellular chain complex      139
Cellular cohomology      202
Cellular homology      139 153
Cellular map      349
Chain      105 108
Chain complex      106
Chain homotopy      113
Chain map      111
Change of basepoint      28 341
Characteristic map      7 519
circle      29
Classifying space      165
Closed manifold      231
Closure-finite      521
Coboundary      198
Coboundary map      191 197
Cochain      191 197
Cocycle      198
Coefficients      153 161 198 462
Cofiber      461
Cofibration      460
Cofibration sequence      398 462
Cohen — Macauley ring      228
Cohomology group      191 198
Cohomology operation      488
Cohomology ring      211
Cohomology theory      202 314 448 454
Cohomology with compact supports      242
Cohomotopy groups      454
Colimit      460 462
Collar      253
Commutative diagram      111
Commutative graded ring      215
Commutativity of cup product      215
Compact supports      242 334
Compact-open topology      529
Compactly generated topology      523 531
Complex of spaces      457 462 466
Compression lemma      346
Cone      9
Connected graded algebra      283
Connected sum      257
Contractible      4 157
Contravariant      163 201
Coproduct      283 461
Covariant      163
Covering homotopy property      60
Covering space      56 321 342 377
Covering space action      72
Covering transformation      70
Cross product      210 218 223 268 277 278
Cup product      249
CW approximation      352
CW complex      5 519
CW pair      7
CYCLE      106
Deck transformation      70
Decomposable operation      497
Deformation retraction      2 36 346 523
Deformation retraction, weak      18
Degree      134 258
Diagonal      283
Diagram of spaces      456 462
Dihedral group      75
DIMENSION      6 126 231
Direct limit      243 311 455 460 462
Directed set      243
Divided polynomial algebra      224 286 290
Division algebra      173 222 428
Dodecahedral group      142
Dold — Thom theorem      483
Dominated      528
Dual Hopf algebra      289
Eckmann — Hilton duality      460
EDGE      83
Edgepath      86
EHP sequence      474
Eilenberg      131
Eilenberg — MacLane space      87 365 393 410 453 475
ENR, Euclidean neighborhood retract      527
Euler characteristic      6 86 146
Euler class      438 444
Exact sequence      113
Excess      499
Excision      119 201 360
Excisive triad      476
Ext      195 316 317
Extension Lemma      348
Extension problem      415
Exterior algebra      217 284
External cup product      210 218
Face      103
Fiber      375
Fiber bundle      376 431
Fiber homotopy equivalence      406
Fiber-preserving map      406
Fibration      375
Fibration sequence      409 462
Finitely generated homology      423 527
Finitely generated homotopy      364 392 423
Five-lemma      129
Fixed point      31 73 114 179 229 493
Flag      436 447
Frame      301 381
Free action      73
Free algebra      227
Free group      42 77 85
Free product      41
Free product with amalgamation      92
Free resolution      193 263
Freudenthal suspension theorem      360
Function space      529
functor      163
Fundamental class      236 394
Fundamental group      26
Fundamental theorem of algebra      31
Galois correspondence      63
General linear group $GL_n$      293
Good pair      114
Gram — Schmidt orthogonalization      293 382
Graph      6 11 83
Graph of groups      92
Graph product of groups      92
Grassmann manifold      226 381 435 439 445
Groups acting on spheres      75 135 391
Gysin sequence      438 444
HNN extension      93
Hocolim      460 462
Holim      462
Homologous cycles      106
Homology      106
Homology decomposition      465
Homology of groups      148 423
Homology theory      160 314 454
Homotopy      3 25
Homotopy equivalence      3 10 36 346
Homotopy extension property      14
Homotopy fiber      407 461 479
Homotopy group      340
Homotopy group with coefficients      462
Homotopy lifting property      60 375 379
Homotopy of attaching maps      13 16
Homotopy type      3
Hopf      134 173 222 281 285
Hopf algebra      283
Hopf bundle      361 375 377 378 392
Hopf invariant      427 447 489 490
Hopf map      379 380 385 427 430 474 475 498
Hurewicz homomorphism      369 486
Hurewicz Theorem      370 372 390
H–space      281 419 420 422 428
Induced fibration      406
Induced homomorphism      34 110 111 118 201 215
Infinite loopspace      397
Invariance of dimension      126
Invariance of domain      172
Inverse limit      312 410 462
Inverse path      27
Isomorphism of actions      70
Isomorphism of covering spaces      67
Iterated mapping cylinder      457 466
J –homomorphism      387
J(X ), James reduced product      224 282 288 289 467 470
Join      9 20 457
Jordan curve theorem      169
K(G,1) space      87
K-invariant      412 475
Klein bottle      51 74 93 102
Kuenneth formula      219 268 274 275 357 432
Lefschetz      131 179 229
Lefschetz duality      254
Lefschetz number      179
Lens space      75 88 144 251 282 304 310 391
Leray — Hirsch theorem      432
Lie group      282
Lift      29 60
Lifting criterion      61
Lifting problem      415
Lim-one      313 411
LIMIT      460 462
Linking      46
Local coefficients: cohomology      328 333
Local coefficients: homology      328
Local degree      136
Local homology      126 256
Local orientation      234
Local trivialization      377
Locally contractible      523 525
Locally finite homology      336
Locally path-connected      62
Long exact sequence: cohomology      200
Long exact sequence: fibration      376
Long exact sequence: homology      114 116 118
Long exact sequence: homotopy      344
Loop      26
Loopspace      395 408 470
Manifold      231 527 529
Manifold with boundary      252
Mapping cone      13 182
Mapping cylinder      2 182 347 457 461
Mapping telescope      138 312 457 528
Mapping torus      53 151 457
Maximal tree      84
Mayer — Vietoris axiom      449
Mayer — Vietoris sequence      149 159 161 203
Milnor      408 409
Minimal chain complex      305
Mittag — Leffer condition      320
Monoid      163
Moore space      143 276 312 320 391 462 465 475
Moore — Postnikov tower      414
Morphism      162
n-connected cover      415
n-connected space, pair      346
Natural transformation      165
Naturality      127
Nerve      257 458
Nonsingular pairing      250
Normal covering space      70
Nullhomotopic      4
Object      162
Obstruction      417
Obstruction theory      416
Octonion      173 281 294 378 498
Open cover      459
Orbit, orbit space      72 457
Orientable manifold      234
Orientable sphere bundle      442
Orientation      105 234 235
Orientation class      236
Orthogonal group O(n)      292 308 435
p-adic integers      313
Path      25
Path lifting property      60
Pathspace      407
Permutation      68
Plus construction      374 420
Poincare      130
Poincare conjecture      390
Poincare duality      241 245 253 335
Poincare series      230 437
Pontryagin product      287 298
Postnikov tower      354 410
Primary obstruction      419
Primitive element      284 298
Principal fibration      412 420
prism      112
Product of $\Delta$ complexes      278
Product of CW complexes      8 524
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