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Whitehead G.W. — Elements of Homotopy Theory
Whitehead G.W. — Elements of Homotopy Theory

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Название: Elements of Homotopy Theory

Автор: Whitehead G.W.

Аннотация:

The writing bears the marks of authority of a mathematician who was actively involved in setting up the subject. Most of the papers referred to are at least twenty years old but this reflects the time when the ideas were established and one imagines that the situation will be different in the second volume. Because of the length, it is unlikely that many people will read this book from cover to cover, but it will be used for reading up on a particular topic or dipping into for sheer pleasure - and the fact that the details may not be quite as expected should add to the enjoyment.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 744

Добавлена в каталог: 02.07.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H_{0}$-space      461
Action (of the fibre on a fibration)      321
Additive cohomology operation      252
Additive homotopy operation      490
Additive relation      365 496 722
Additive relation, null      727
Adem relations      403
Adjoint functor      21
Adjoint map      21
Adjunction space      22
Algebra, alternative      688
Algebra, cohomology      147
Algebra, Hopf      146 150
Algebra, of stable operations      393
Algebra, Pontryagin      145
Algebra, Steenrod      393
Amplification      427
Antiloop operator      138
Antisuspension operator      130
Aspherical      224
Associated bundle      305
Associated principal      305 678
Associator      688
Attaching map      48
Baer product      601
Barycenter      10
Base point, non degenerate      28 98
Base space (of a fibration)      29
Biproduct      720
Blakers homology groups      171
Blakers — Massey homotopy excision theorem      366
Bockstein operator      251 393
Bonding map      421
Bonding map, for a map      446
Bonding sequence      421
Bundle of groups      257
Bundle of groups, constant      263
Bundle of groups, simple      263
Canonical extension      329 515
Cap product      349 508
Carrier      50
Cartan product formula      397
Cayley algebra      676 686
Cayley algebra, automorphisms of      690
Cayley projective plane      677 700
Cell (of a cellular extension)      48
Cell (of a cellular extension) (of a CW-complex)      50
Cell (of a cellular extension), dual      507
Cell (of a cellular extension), oriented      82 168
Cell complex, regular      81 582 599
Cellular approximation theorem      77
Cellular extension      48
Cellular extension, homotopy groups of      211
Cellular homotopy      77
Cellular map      76
Central chain      462
Characteristic class (of a space)      236
Characteristic class (of a vector bundle)      307 308
Characteristic element      194
Characteristic map (in a cellular extension)      48
Characteristic map (of a fibration)      317
Circulator      696 714
Classification Theorem (for partial liftings)      302
Classification Theorem, Eilenberg      243
Classification Theorem, Hopf — Whitney      244
Classifying space      305 679
Clifford algebra      686
Clifford algebra, group      682
Coalgebra      143
Codomain      722
Coefficient group      573
Coefficient group, homomorphism      251 393
Cofibration      7
Cogrouplike space      122
Coherent family      27
Cohomology algebra      147
Cohomology algebra, of Eilenberg — MacLane spaces      670
Cohomology algebra, of the exceptional Lie group $G_{2}$      361 410
Cohomology algebra, of the Grassmannian G(n)      362
Cohomology algebra, of the loop space of a sphere      326
Cohomology algebra, of the rotation group      346
Cohomology algebra, of the Stiefel manifold      348
Cohomology algebra, of the symplectic group      342
Cohomology algebra, of the unitary group      342 345
Cohomology class, decomposable      148 383
Cohomology class, decomposable, primitive      148 383
Cohomology class, decomposable, reductive      147 383
Cohomology class, decomposable, transgressive      383
Cohomology equivariant      279
Cohomology operation      250 385
Cohomology operation, additive      252
Cohomology operation, decomposable      407
Cohomology operation, functional      540
Cohomology operation, secondary      454
Cohomology operation, stable      391
Cohomology operation, suspension of      386
Cohomology theory      596
Cohomology theory, additive      595 597
Cohomology theory, complete      595 597
Cohomology theory, isotropic      595 597
Cohomology theory, proper      595 597
Cohomology theory, reduced      594
Cohomology with local coefficients      270
Coimage      722
Coindeterminacy      722
Cokernel      722
Combinatorial extension      333 549
Commutator      462
Commutator map      463
Commutator map, special      463
Composite (of additive relations)      722
Composition product      126 478
Composition product, additivity of      479 494 534 551
Compressible      70
Compressible, right      74
Cone      105
Configuration      8
Connecting map (for a fibration)      141
Connecting map (for an NDR-pair)      137
Connection      29
CONVERSE      722
Coordinates, barycentric      10
Coordinates, homogeneous      676
Coproduct      121
Coshear map      122
Cross product, cohomology      67 654
Cross product, homology      64
Cross section      189
Cross section, relative      291
Crossed homomorphism      275
Crossed homomorphism, principal      276
Cup product      88 349 668
Cup product, functional      498
Cup square      251 394
CW-approximation      222 249 462
CW-approximation, of a pair      224 299
CW-complex      50
CW-complex, relative      50
CW-complex, relative, chain complex of      61
CW-decomposition      50
Decomposable cohomology class      148 383
Decomposable element of an algebra      152
Decomposable homology class      145 383
Deformable      23
Deformation, retracting      24
Deformation, retraction      24
Degree, Brouwer      13
Detectable      407
Difference cochain      231
Difference cochain (of partial liftings)      296
Difference primary (of partial liftings)      299
Direct product      717
Direct Product Theorem      598
Direct Product Theorem, General      598
Direct product, weak      721
Direct sum      718
Direct sum, strong      721
Direct, Sum Theorem      58 581
Direct, Sum Theorem, General      59 581
Divided polynomial ring      325
Domain      722
Dominate      23
DR-pair      22
EHP-sequence      548
Eilenberg Classification Theorem      243
Eilenberg Classification Theorem, Extension Theorem      239
Eilenberg Classification Theorem, homology groups      171
Eilenberg Classification Theorem, Homotopy Theorem      243
Eilenberg — Mac Lane space      239 244 385 417
Eilenberg — Mac Lane space, cohomology of      670
Eilenberg — Mac Lane space, homology of      652
Equivalence, fibre homotopy      38
Equivalence, homology      182
Equivalence, homotopy      23
Equivalence, weak homotopy      181
Equivalence, weak homotopy (of pairs)      219
Evaluation map      20 104 516
Exact couple      608
Exact couple, derived      610
Exact couple, maps and homotopies of      612
Exceptional Jordan algebra      695
Exceptional Lie group $F_{4}$      701
Exceptional Lie group $G_{2}$      690
Exceptional Lie group $G_{2}$ cohomology of      360 410
Expanding sequence      27
Extension      4
Extension, canonical      329 515
Extension, combinatorial      333 549
Extension, theorem (for partial liftings)      302
Factorization problem      3 4
Fibration      8 29
Fibration, coorientable      651
Fibration, equivalent to a map      42
Fibration, induced      37
Fibration, n-connective      417
Fibration, of pairs      623
Fibration, orientable      349 649
Fibration, spherical      195
Fibration, trivial      31
Fibration, vs. fibre bundle      33
Fibre      29
Fibre, bundle      33 678
Fibre, bundle, associated      305
Fibre, homotopically trivial      38
Fibre, homotopy equivalence      38
Fibre, homotopy sequence      188
Fibre, homotopy type      38
Fibre, space      29
Filtered space      28
Folding map      116
Free homotopy      103
Free homotopy along a path      98
Free loop      370
Free map      103
Free path      106
Free resolution      226 281 562
Free space      103
Freudenthal suspension theorem      369
Function space      20 104
Fundamental group, operations of      100 101 164 186
Fundamental groupoid      99 257
Gauss map      679
Grassmann manifold      11
Grassmann manifold, complex      12
Grassmann manifold, homotopy groups of      204
Grassmann manifold, quatemionic      12
Grassmannian, G(n), cohomology of      362
Group extensions      562
Grouplike space      118 461
Gysin sequence      359 671
Gysin sequence, Theorem      356
H'-map      126
H'-space      121
H'-space, homotopy associative      122
H-fibration      338
H-map      120
H-pair      120
H-space      116
H-space, homotopy associative      117
H-space, strictly associative      117
Height (of an element of an algebra)      153
Hilton — Milnor Theorem      515
Homeomorphism, relative      22
Homology class, decomposable      145 383
Homology class, primitive      143 383
Homology class, reductive      143 383
Homology class, spherical      143 247
Homology class, transgressive      383
Homology equivalence      182
Homology equivariant      279
Homology of groups      227 281
Homology operation      413
Homology suspension      365 373
Homology Suspension Theorem      377
Homology theory      579
Homology theory, additive      574 579
Homology theory, complete      574 580
Homology theory, isotropic      574 580
Homology theory, proper      573 579
Homology theory, reduced      572
Homology with local coefficients      265 269
Homomorphism (of bundles of groups)      263
Homotopy      5 268 271
Homotopy class      6
Homotopy class, primitive      494
Homotopy group      125
Homotopy group, relative      159
Homotopy operation      490
Homotopy operation, additive      493
Homotopy resolution      421
Homotopy resolution of a map      446
Homotopy resolution, canonical      426
Homotopy sequence of a fibration      187
Homotopy sequence of a pair      162
Homotopy sequence of a triple      163
Homotopy Theorem, Eilenberg      244
Homotopy Theorem, Eilenberg, for partial liftings      302
Homotopy, Addition Theorem      174
Homotopy, cellular      77
Homotopy, equivalence      23
Homotopy, Excision Theorem (Blakers — Massey)      366
Homotopy, extension problem      7
Homotopy, free      103
Homotopy, free along a path      98
Homotopy, inverse      23
Homotopy, lifting extension problem      34
Homotopy, lifting problem      8 29
Homotopy, Map Excision Theorem      369
Homotopy, relative to a subset      5
Homotopy, stationary      6
Homotopy, vertical      291
Hopf algebra      146 150
Hopf construction      502
Hopf fibration      188 394 675 709
Hopf invariant      494
Hopf retromorphism      509
Hopf — Hilton homomorphism      534
Hopf — Hilton invariant      534
Hopf — James invariant      336 548
Hopf — Whitney Classification Theorem      244
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