Авторизация
Поиск по указателям
McCleary J. — A user's guide to spectral sequences
Обсудите книгу на научном форуме Нашли опечатку?
Название: A user's guide to spectral sequencesАвтор: 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: 2001Количество страниц: 561Добавлена в каталог: 05.03.2005Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Maximal 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 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
Реклама
-perfect submodule 
invariants 
|
|
О проекте