Massey W.S. — A basic course in algebraic topology :: Электронная библиотека попечительского совета мехмата МГУ

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Massey W.S. — A basic course in algebraic topology

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Название: A basic course in algebraic topology

Автор: Massey W.S.

Аннотация:

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are: the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 428

Добавлена в каталог: 07.11.2005

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Предметный указатель

Acyclic models, method of      288 298
Alexander duality theorem      374
Alexander, J.W.      322 349 391
Algebraic homotopy      167
Algebraic mapping cone      258—259
Almost exact sequence      387
Almost simplicial complex      249
Anticommutative product      343
ARC      36
Augmentation      161 288
Automorphisms of a covering space      130 134—135
Axiomatic approach to homology theory      184
Ball, n-dimensional      xv 188
Basis for a free group      78
Betti group      367
Betti numbers of a space      224
Betti, E.      156
Bockstein operator      268 309
Borsuk — Ulam theorem      138—140 397
Boundaries, group of      160
Boundary of a cell      239
Boundary of a pair      171
Boundary operator      160
Boy, W.      33
Branched covering space      144—145
Brouwer fixed point theorem      50 188
Brouwer, L.E.J.      186 211
Cap product      328 332
Cap product in a product space      342—343
Casson, A.      32
Cayley projective plane      403
Cech — Alexander — Spanier cohomology      371
Cech, E.      322 349
Cell, n-dimensional      226
Cellular map      232
Cellular map, induced homomorphism      236—237
Chain complex      254
Chain complex, acyclic      288
Chain complex, augmented      265 288
Chain complex, Positive      288
Chain groups of a CW-complex      233
Chain homotopy      167 256
Chain map      255
Characteristic map      236
Classification theorem for compact surfaces      9 26
Coboundaries      307
Coboundary operator      306
Cochain with compact support      358 417
Cochain, complex      306
Cochain, homotopy      306
Cochain, map      306
Cocycles      307
Coefficient homomorphism      267 309
Coherent orientations      250
Cohomology group      307
Cohomology sequence of a map      401
Cohomology theory, development of      322
Cokernel      xvi
Commutator      77
Compact pair      211
Complex, CW      228—232
Complex, regular      243—244
Connected sum      7—9 32
Connecting homomorphism      257
Connectivity, arcwise or pathwise      36
Connectivity, local arcwise      36
Connectivity, semilocal simple      142
Connectivity, simple      45
Contractible space      45 168
Convex set      46
Covering space      117—146
Covering space of a topological group      129 135
Covering space, existence theorem for      142—144
Covering space, induced over a subspace      122
Covering transformation      130
Cross product      325 330
Crowell, R.H.      113
Cup product      325 331—332 369
Cup product in a product space      342
Cup product in projective spaces      395—397
CW-complex      228—232
Cycles      160
Defect of singular homology theory      335
Deformation retract      45 168
Degenerate singular cube      159
Degree of a map      189—190
deRham complex      411
DeRham's theorem      413
deRham, G.      417
Diagonal map      299 328
Differentiable singular chains      408
Differentiable singular cube      408
Dimension of a CW-complex      229
Direct limit      359
Direct product      60—61
Disc, n-dimensional      xv 188
Divisible group      311
Edge of a graph      192
Eilenberg — Zilber theorem      284
Eilenberg, S.      184
Elementary neighborhood      118
Epimorphism      xv
Equivariant map      420—421
Euler characteristic of a CW-complex      235—236
Euler characteristic of a graph      194
Euler characteristic of a surface      26—30
Exact homology sequence of a chain map      259
Exact homology sequence of a pair      171
Exact sequence      xvi
Exact sequence of chain complexes      257
Excision property      175
Excisive couple      301
Ext functor      311—313
Face of a cell      243
Faces of a singular cube      159
Fibre bundles      145
Fibre spaces      145
Five lemma      184
Fox, R.H.      145
Free Abelian group      63—70
Free group      75—78
Free product of groups      71—74
Free product of groups with amalgamated subgroups      113
Freedman, M.      32 114
Fundamental group      35—41 86—113
Fundamental group of a circle      47
Fundamental group of a compact 4-manifold      114—115
Fundamental group of a compact surface      96—103
Fundamental group of a connected sum of manifolds      95
Fundamental group of a covering space      126—127
Fundamental group of a figure "8" curve      91—92
Fundamental group of a product space      52—53
Fundamental group of a punctured disc or plane      92—93
Fundamental group of a topological group      63
Fundamental group of a union of circles      93
Fundamental group of real projective n-space      137
Fundamental group of the complement of a knot      103—108
Fundamental group, relation to 1st homology group      217—219
Generators of a group      63—64
Genus of a surface      30
Graded module      344
Graded ring      343
Graph      192
Group of a knot      104
Group of operators      419
Heegard, P.      156
History of algebraic topology      156
Homogeneous space      421
Homogeneous space, automorphism group of a      422—423
Homology group, relative      170 173—175

Homology group, singular      160
Homology sequence of a pair      171
Homomorphism of covering spaces      130
Homomorphism, induced by a continuous map      42 163—164
Homotopic maps      43
Homotopy      43
Homotopy, classes      166
Homotopy, differentiable      409
Homotopy, equivalence      57 168
Homotopy, groups of a covering space      145—146
Homotopy, type      57 168
Homotopy, type vs. topological type      114
Hopf invariant      402—404
Hopf, H.      405
Hurewicz, W.      58 185
Immersion      32—33
Incidence numbers      240 245 247—248
Induced homomorphism      42 163—164
Injective group      312
Injective resolution      313
Inner product      310 324
Invariance of domain theorem      216
Inverse limit      415
Isomorphism of groups      xv
Isotropy subgroup      421
Jordan curve theorem      146 211
Jordan — Brouwer separation theorem      215
Klein bottle      7—8
Knot      103
Kolmogoroff, A.N.      322 349
Kunneth theorem      285
Lebesgue number      48 180
Lefschetz — Poincare duality theorem      377 379
Lefschetz, S.      349 391—392
Lifting of maps      127—129
Lifting of paths      123—125
Local arcwise connectivity      36
Local homeomorphism      122
Local homology group      191
Local orientation      351
Loop      41
Magic formula      287
Manifold with boundary      375
Manifold, definition      2 350
Manifold, orientable vs. non-orientable      3—5 352
Map of pairs      173
Map of pairs, homotopic      173—174
Mapping cone      399
Mapping cylinder      399
Markov, A.A.      33 115
Mayer — Vietoris sequence      207—208 266 320—321
Mayer — Vietoris sequence with compact supports      361—362
Mayer — Vietoris sequence, relative      338
Moebius strip      3—4
Moise, E.      32
Monomorphism      xv
Mysterious facts of life      334
n-dimensional manifold      2 350
n-dimensional manifold with boundary      375
Noether, E.      224
Normalizer of a subgroup      422
Number of sheets of a covering space      125 133
Orientable manifold      3—5 352
Orientation of a cell      239 247—248
Orientation of a manifold      3 351
Orientation of a product complex      281
Oriented edges      195
Paths      36
Paths, closed      41
Paths, equivalence of      36—37
Paths, product of      37
Permutation groups      419—423
Poincare conjecture      113—114
Poincare duality theorem      350 360 365
Poincare groups      41
Poincare series      303
Poincare, H.      58 113—114 156 391
Pontrjagin, L.      391
Presentation of a group      78—81
Product of groups, direct      60—61
Product of groups, free      71—74
Product of groups, tensor      254
Product of groups, weak      61—63
Projection      118
Projective group      311
Projective plane Cayley      403
Projective plane, real      6—7
Projective resolution      313
Projective spaces      230—232
Projective spaces, complex      231
Projective spaces, cup products in      395—397
Projective spaces, homology groups of      236 399
Projective spaces, quaternionic      232
Projective spaces, real      230—231
Proper map      359
Properly discontinuous group      136
Pseudomanifold      249
Pseudomanifold, orientable      251
Rado, T.      14 32
Ramified covering space      144—145
Rank of a free abelian group      69
Rank of a free group      78
Rank of an abelian group      235—236
Reduced cohomology group      308
Reduced homology group      161
Reduced word      77
Regular covering space      134
Regular CW-complex      243—244
Relative homology group      169—170
retract      44 166
Riemann, G.F.B.      156
Seifert, H.      113
Seifert, H., theorem of      87—90
Sheets of a covering space      125 133
Simplex, singular      298
Simplicial complex      see "Almost simplicial complex"
Simplicial singular chains      298
Singular cube      158
Singular cycle      155 160
Singular homology group      160
Skeleton of a CW-complex      229
Skew commutative product      343
Slant product      327 330
Smale, S.      114
Small of order $\mathscr{U}$       176
Sphere, n-dimensional      xv 186
Split exact sequence      263
Splitting homomorphism      258 263
Steenrod, N.E.      184 405
Subcomplex of a CW-complex      232
Subdivision operator      179 410
Support of a chain      317
Support of a cochain      318—319
Support of a differential form      417
Support, compact      358
surface      5
Suspension of a map      405
Suspension of a space      405
Symmetric group      419
Taut subspace      370
Tensor product of chain complexes      282
Tensor product of graded rings      347—348
Tor functor      270
Torsion, coefficients of a group      70
Torsion, coefficients of a space      224
Torsion, subgroup      70
Torus      5
Torus, knot      104—105
Transformation group      419—423
Triad      337

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