McCleary J. — A user's guide to spectral sequences :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

McCleary J. — A user's guide to spectral sequences

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: A user's guide to spectral sequences

Автор: McCleary J.

Аннотация:

Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Язык:

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 561

Добавлена в каталог: 05.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Maximal $\pi$ -perfect submodule      345
Maximal augmentation      356
Maximal torus      278
May spectral sequence      441ff. 510
May's tables      447
Method of killing homotopy groups      203
Miller spectral sequence      499
Milnor $\bar{\mu}$ invariants      310
Milnor spectral sequence      268
Minimal resolution      379
Mittag — Leffier condition      79
Mixed Hodge structure      519
Mod p finite H-space      474
Mod r homotopy groups      480
Module over a differential graded algebra      225
Module spectrum      497
Monogenic Hopf algebra      213
Moore space      463 480
Moore spectral sequence      268
Morava K-theory      482
Morphism of bundles of groups      165
Morphism of exact couples      74
Morphism of fibrations      112
Morphism of fibre bundles      209
Morphism of filtered differential graded modules      66
Morphism of simplicial objects      104
Morphism of spectral sequences      65
Morse theory      304
Motivic cohomology      522
Nerve of a category      502
Nilpotent completion      362
Nilpotent group      344
Nilpotent module      345
Nipotent space      346
Nishida's nilpotence theorem      407
Normed algebra      366
Omega-spectrum      120
Operad      297
Oriented cobordism ring      414
p-component of a group      370
p-divisble elements in a group      459
Path-loop fibration      112 157
Perfect field      213
Periodicity theorem      431
Perturbation theory      297
Poincare series      14 204 310 509
Polynomial cohomology      275
Pontrjagin — Thom construction      409
Pontryagin product      125
Positive scalar curvature metric      451
Postnikov system      120
Postnikov tower      182 327 352
Presentation of an algebra      281
Primitives      124
Principal bundle      209
Principal fibration      352
Principal refinement      352
Pro-isomorphism      362
Projective line      113
Projective module      51
Projective resolution      51
Proper exact sequence      226
Proper projective resolution      55 237 238
Pullback of a fibration over a map      114
Quadratic construction      425
Quillen spectral sequence      488
R-completion      361
R-good space      361
R-nilpotent space      363
Rank of a Lie group      277
Rational Hurewicz theorem      161
Real projective space      94
Reduced suspension      98
Rees system      88
Regular CW-complex      100
Regular sequence      283
Representable functor      495
Restricted Lie algebra      441
Reverse Adams spectral sequence      450 496
Ring spectrum      497
Rothenberg — Steenrod spectral sequence      268
Second Eilenberg-Moore theorem      250
Secondary cohomology operation      375
Semifree resolution      287
Serre exact sequence      145
Serre fibration      109
Sh-module      295
Shc (strongly homotopy commutative) algebra      295
Sheaf      222 515
Shm (strongly homotopy multiplicative) map      294
Short exact sequence of Hopf      339
Shuffle      123
Simple system of generators      154
Simple system of local coefficients      138
Simplicial approximation theorem      109
Simplicial homotopy      106
Simplicial identities      103
Simplicial object in a category      104
Simplicial replacement of a functor      502
Simplicial set      103
Singular complex      104
Skeleton      93
Slide products      311
Slope spectral sequence      518
Solid ring      361
Space of based loops      95 156
Space of based paths      111
Space of paths      156
Spectral datum      88
Spectral ring      45
Spectral sequence      4
Spectral sequence, Adams — Novikov      499
Spectral sequence, adiabatic      519
Spectral sequence, algebraic May      87
Spectral sequence, Arnol'd — Vassiliev      505
Spectral sequence, Atiyah      496
Spectral sequence, Atiyah — Hirzebruch      496
Spectral sequence, bar      268
Spectral sequence, Barratt      488
Spectral sequence, Bloch — Lichtenbaum      522
Spectral sequence, Bockstein      38 455ff.
Spectral sequence, Bousfield-Kan      361
Spectral sequence, Bousfield-Kan homology      503
Spectral sequence, Brown — Gersten — Quillen      521
Spectral sequence, C-spectral sequence      519

Spectral sequence, Cartan — Leray      160 337ff.
Spectral sequence, change-of-rings      387 508
Spectral sequence, composite functor      514
Spectral sequence, conditionally convergent      76
Spectral sequence, Connes      510
Spectral sequence, convergence of      5 33
Spectral sequence, descent      521
Spectral sequence, dihomology      505
Spectral sequence, EHP      495
Spectral sequence, Eilenberg — Moore, for generalized theories      498
Spectral sequence, elementary      86
Spectral sequence, equivariant Leray — Serre      502
Spectral sequence, Federer      490
Spectral sequence, Froelicher      518
Spectral sequence, Grothendieck      514
Spectral sequence, Hochschild — Serre      511
Spectral sequence, Hodge — de Rham      517
Spectral sequence, homology Eilenberg — Moore      268
Spectral sequence, Hurewicz      490
Spectral sequence, hypercohomology      514
Spectral sequence, image computing      506
Spectral sequence, Kuenneth      56
Spectral sequence, Leray      515
Spectral sequence, Leray — Serre, for generalized theories      498
Spectral sequence, local-to-global      515
Spectral sequence, Lyndon — Hochshild — Serre      340ff.
Spectral sequence, May      441ff. 510
Spectral sequence, Miller      499
Spectral sequence, Milnor      268
Spectral sequence, Moore      268
Spectral sequence, of a bisimplicial group      488
Spectral sequence, of a double complex      48
Spectral sequence, of algebras      12 45
Spectral sequence, of cohomological type      29
Spectral sequence, of homological type      28
Spectral sequence, Quillen      488
Spectral sequence, reverse Adams      450 496
Spectral sequence, Rothenberg — Steenrod      268
Spectral sequence, slope      518
Spectral sequence, Universal Coefficient      497 514
Spectral sequence, unstable Adams      491ff.
Spectral sequence, van Est      511
Spectral sequence, van Kampen      489
Spectral system      461
Spectrum      408
Spike      478
Stable cohomology operation      127
Stable filtration      12
Stable higher order cohomology operation      375
Stable homology      499
Stable homotopy group      366
Stable homotopy groups of spheres      99
Stable mappings      99
Stable object      408
Staircase argument      307
Steenrod algebra      128
Steenrod operations      195
Steenrod operations, on Ext      385
Stiefel manifold      151 285
Stiefel — Whitney classes      217
Strongly convergent filtration      69
Structure group      208
Subcomplex      94
Sullivan conjecture      504
Supplementation      124
Suspension      94
Suspension homomorphism      98
Suspension isomorphism      128
Sylow subgroup      342
Symplectic groups      179
System of local coefficients      164
Tangent bundle      113
Tensor product of differential (bi)graded modules      44
Theorem of Borel and Serre      142
Theorem of Bott      456
Theorem of Cartan and Serre      197
Theorem of Hopf      456
Theorem of Morse      158
Thom isomorphism theorem      411
Thom space      409
Thom spectrum      410
Toda bracket      429
Toda's tables      446
Torsion-free space      456
Total complex      24 47
Total space      110
Totally nonhomologous to zero      148
Tower of submodules      30
Transgression      185ff.
Transgressive element      85 192
Transpotence      194
Triple      322
Trivial fibration      112
Truncated polynomial algebra      144
Twisting cochain      223
Two-stage Postnikov system      291
ULC      160
UNIT      123
Universal bundle      210
Universal Coefficient spectral sequence      497 514
Universal coefficient theorem      50
Universal enveloping algebra      441
Unnormalized bar construction      247
Unraveled exact couple      40
Unstable Adams spectral sequence      491ff.
Upside-down Postnikov system      203
Van Est spectral sequence      511
Van Kampen spectral sequence      489
Vanishing line      431
Variational bicomplex      519
Vassiliev invariants      505
Very nice space      492
Wang sequence      26 145
Weak topology      93
Weakly contractible space      120
Weakly convergent filtration      62
Wedge axiom      496
Weyl group      279
Whitehead product      303
Whitehead theorem      96
Whitehead theorem, generalized      348ff.
Whitney sum      217 410
Word of warning      34
Yoneda product      381
Zeeman comparison theorem      82 198 359

1 2

О проекте