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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
Hopf — Whitney Extension Theorem      238
Hurewicz map      166
Hurewicz Theorem      178
Idempotent, primitive      698
Image      722
Incidence isomorphism      82 169
Incidence isomorphism, general      582 599
Incidence number      79 82
Incidence system      84
inclusion      4 20 269 271
Indeterminacy      722
Injection      55 269 271
Integers, twisted      285
Intersection number      509
Inverse limit, derived      271
Inverse limit, of fibrations      432
Inverse, homotopy      23
J-adjoint      516
J-extension      516
J-homomorphism      504
Jacobi identity (for Samelson products)      470
Jacobi identity (for Whitehead products)      478
Kernel      722
LADDER      724
Left exact sequence of spaces      127
Lens space      91 94
Lifting      4
Lifting, extension problem      34 291
Lifting, partial      291
Linking number      509
Local coefficient system      257
Local coefficient system, in G(n)      306
Local coefficient system, twisted      285 306
Loop      106
Loop, free      370
Loop, measured      114
Loop, space      43
Lower central series      462
Map, attaching      48
Map, cellular      76
Map, characteristic (in an n-cellular extension)      48
Map, characteristic (of a fibration)      317
Map, Excision Theorem      57 580 598
Map, n-anticonnected      444
Map, n-connected      181
Map, simple      447
Map, simultaneous attaching      48
Map, standard      14
Map, u-admissible      185 626
Mapping cone      23 106
Mapping cone (of a chain map)      566
Mapping cylinder      23 106
Mapping cylinder, relative      421
Mapping fibre      43
Maximal torus      677
Measured loop      114
Measured path      107
Mobius inversion formula      514
Moore space      370
n-anticonnected map      444
n-anticonnected space      418
n-connected map      181
n-connected pair      70
NDR-filtration      28
NDR-filtration of a pair      604
NDR-pair      22
Nilpotent      462
Obstruction      229
Obstruction, primary      236
Obstruction, primary (to a homotopy)      240
Obstruction, primary (to a lifting)      298
Obstruction, secondary      453
Obstruction, set      234 450
Obstruction, to a partial lifting      292
Orientable fibration      349 649
Orientable manifold      507
Orientation bundle      263
Orientation coherent      169
Orientation local      258
Orientation of a cell      82 168
Orientation of a regular cell complex      82
Orientation of a sphere      168
Orthogonal group      see also “rotation group” 10
Pair, n-connected      70
Pair, simple      116
Path      106
Path, free      106
Path, measured      107
Poincare series      322
Polarization      681 687
Pontryagin algebra      145
Pontryagin algebra, of J(W)      323
Pontryagin algebra, of the rotation group      347
Pontryagin algebra, of the symplectic group      343
Pontryagin algebra, of the unitary group      343 345
Postnikov invariant      423
Postnikov system      431
Postnikov system of a space      423
Postnikov system, fibred      432
Power-associative      696
Primitive cohomology class      148 383
Primitive element of a coalgebra      152
Primitive homology class      143 383
Primitive homotopy class      494
Primitive idempotent      698
Primitive with respect to a map      504
Principal associated bundle      305 678
prism      105 268 271
Proclusion      4 20
Product, basic      511
Product, cap      349 508
Product, cartesian      19
Product, categorical      19
Product, cup      88
Product, external      120
Product, in an H-space      117
Product, of CW-complexes      50
Product, of regular cell complexes      88
Product, weak      28 208 419
Projective plane, Cayley      677 700
Projective space, complex      12
Projective space, complex, cohomology of      90
Projective space, quaternionic      12
Projective space, real      12
Projective space, real, cohomology of      89
Pure subgroup      563
Rank (of a basic product)      512
Rank (of a compact Lie group)      678
Reduced join      103 480
Reduced product      326
Reductive cohomology class      147 383
Reductive homology class      145 383
Reindexing      573
Relational chain complex      727
Resolution, free      226 280 562
Resolution, homotopy      421 426 446
Resolving sequence      421
Resolving sequence, for a map      446
retract      24
Retract, deformation      24
Retraction, deformation      24
Right exact sequence of spaces      127
Rotation group      10
Rotation group, cohomology of      346
Rotation group, full      10
Rotation group, homology of      347
Rotation group, homotopy groups of      200
S-map      551
Samelson product      467
Samelson product, and Whitehead product      476
Seam homomorphism      497
Secondary boundary operator      555
Secondary cohomology operation      454
Secondary obstruction      453
Sectional element      194
serial number      512
Serre exact sequence      365 649
Shear map      118 461
Simple map      447
Simple pair      116
Simple space      116 421
Simplex, singular      10
Skeleton      50
Smash product      see “reduced join”
Space, associated compactly generated      18
Space, cogrouplike      122
Space, compactly generated      18
Space, filtered      28
Space, free      103
Space, grouplike      118 461
Space, n-anticonnected      418
Space, n-connected      178
Space, simple      116 421
Spanier — Whitehead category      552
Special triple      691
Spectral sequence      610
Spectral sequence, Atiyah — Hirzebruch      640
Spectral sequence, Leray — Serre      645
Spectral sequence, of a fibration      628 630
Spectral sequence, of a filtered pair      614 616
Spectral sequence, products in      654
Spherical fibration      195
Spherical homology class      143 247
Spin representation      705
Spinor group      684
Stable cohomology operation      391
Stable cohomotopy module      552
Stable homotopy module      552
Stable homotopy ring      552
Stable homotopy ring, commutativity of      553
Steenrod algebra      393
Steenrod algebra, action of on complex projective space      409
Steenrod algebra, action of on first exceptional Lie group G2      410
Steenrod algebra, action of on real projective space      399
Steenrod algebra, action of on Stiefel manifolds      400
Steenrod algebra, action of on unitary group      410
Steenrod squares      395
Stiefel manifold      11
Stiefel manifold quaternionic      12
Stiefel manifold, cohomology of      348
Stiefel manifold, complex      12
Stiefel manifold, homotopy groups of      203
Stiefel — Whitney classes      308
Stratification      459
Structural map      317
Subcomplex      51
subspace      20
Suspension      105 496 544 724
Suspension Theorem (Freudenthal)      369
Suspension, category      552
Suspension, category homology      365 373
Symplectic cohomology of      342
Symplectic full      12
Symplectic group      12
Symplectic homology of      343
Thom class      349
Thom isomorphism theorem      350
Topology, weak      27
Total singular complex      10
Total singular complex, geometric realization of      94 208
Total space (of a fibration)      29
Track group      97
TRANSFER      384
Transgression      496 648 724
Transgressive (co)homology class      383
Triad, NDR—      55
Triad, proper      55
Triality, Principle of      712
Trivialization      40
Twisted integers      285
Unitary cohomology class      567
Unitary group      12
Unitary group unimodular      12
Unitary group unimodular, (co)homology of      345
Unitary group, cohomology of      342
Unitary group, full      12
Unitary group, homology of      343
Unitary group, homotopy properties of      205
Universal example      30 165 175 232 485 491 534 559
van Kampen theorem      58 94
Vector bundle, orthogonal      305
Vector field problem      201 400
Vector representation      682
Wang sequence      319 336 671
Weak homotopy equivalence      181 221
Weak homotopy type      221
Weak product      28 208 419
Weakly contractible      220
Weight (of a commutator)      463
Weight (of a monomial)      511
Whitehead product      472 482
Whitehead theorem      181
Whitney classes of a vector bundle      307
Whitney classes, universal      308
Witt formulae      514
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