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



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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: en

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
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Предметный указатель
$cup_1$ product      175 288 453
$\Pi$-algebra      489
$\pi$-complete space      348
$\pi$-module      334
$\pi$-perfect      345
Abelian category      514ff.
Action of a graded algebra      17
Action of a graded algebra on a spectral sequence      18
Adams resolution      393ff.
Adams — Novikov spectral sequence      499
Adem relations      129 367
Adiabatic spectral sequence      519
Adjoint function      110
Admissible product      130
Admissible sequence      196
Alexande — -Whitney map      122 167
Algebraic de Rham complex      517
Algebraic May spectral sequence      87
Analyzer      488
Approximation theorem      439
Arnol'd — Vassiliev spectral sequence      505
Aspherical space      339
Associated graded module      4 31
Associated principal bundle      209
Atiyah spectral sequence      496
Atiyah — Hirzebruch spectral sequence      496
Attaching map      92
Augmentation      123
Bar construction      242ff. 292 335
Bar spectral sequence      268
Barratt spectral sequence      488
Barratt — Puppe sequence      97
Base space      110
Basic goal      3
Bialgebra      126
Bigraded algebra      11
Bisimplicial set      225
Bloch — Lichtenbaum spectral sequence      522
Bockstein homomorphism      127 455
Bockstein spectral sequence      38 455ff.
Borel construction      501
Borromean rings      304
Bounded filtration      34
Bousfield-Kan homology spectral sequence      503
Bousfield-Kan spectral sequence      361
Bredon (co)homology      501
Browder's theorem      473
Brown — Gersten — Quillen spectral sequence      521
Brown — Peterson spectra      500
BRS cohomology      520
Brunnian links      309
Bundle of groups over a space      164
C -spectral sequence      519
C*-algebra      523
Cartan formula      128
Cartan — Eilenberg system      58 461
Cartan — Leray spectral sequence      160 337ff.
Caveat      28 29
Cell decomposition      93
Cell-complex      93
Cellular approximation theorem      94
Cellular chain complex      100
Cellular differential      100
Cellular homology      100
Cellular map      94
Chain homotopy of order k      87
Change-of-rings spectral sequence      387 508
Change-of-rings theorem      280 438
Characteristic mapping      93
Characteristic ring      213
Chern classes      220 230
Classifying space      210
Coalgebra      124
Coassociativity      123
Cobar construction      379 491
Cobordism      408
Cocommutativity      124
Cocomplete category      67
Coefficients of a generalized theory      495
Coexact sequence      278
Cofibrant space      114
Cofibration      96
Coherent system of algebras      461
Cohomology of an algebra      378
Cohomology operation      126
Coinvariants      335
Colimit      67
Collapse of a spectral sequence      7 31
Collapse theorem for Eilenberg — Moore spectral sequence      275
Comodule over a coalgebra      271
Complementary degree      4
Complete category      67
Complete filtration      69
Complete intersection      283
Completion      72 343 345
Complex cobordism      414
Composite functor spectral sequence      514
Composition product, on $\{X,X\}_*$      403
Composition product, on Ext      380
Comultiplication      123
Conditionally convergent spectral sequence      76
Cone      94
Connective generalized theory      496
Connes spectral sequence      510
Construction      194
Convergence as a graded algebra      12
Convergence as an algebra      45
Convergence of a spectral sequence      5 33
Convergence to a module over a graded algebra      18
Cosimplicial object      322
Cosimplicial replacement of a functor      503
Cosimplicial resolution      323
Counit      123
Countable CW-complex      94
Cup product      124
CW-complex      93
Cyclic homology      510
Deficiency of an algebra      283
Deficiency of H in G      284
Defining system      305
Degeneracy map      103
Derivation      11
Derived category      523ff.
Derived couple      38
Descent spectral sequence      521
Desuspension      259
Detected by a higher order operation      374
Diagonal action of the Steenrod algebra      326
Diagonal map      123
Difference homomorphism      298
Differential bigraded algebra      44
Differential bigraded module      4 28
Differential graded algebra      11 44 235
Differential Hopf algebra      470
Dihomology spectral sequence      505
DIMENSION      93
Direct limit      67
Divided power algebra      27 253 385
Division algebra      113 366
Doubeault cohomology      518
Double complex      47
Dyer — Lashof algebra      326
E-algebra      283
Effective action      208
EHP sequence      494
EHP spectral sequence      495
Eilenberg — Mac Lane space      118
Eilenberg — Mac Lane spectrum      120
Eilenberg — Moore spectral sequence for generalized theories      498
Eilenberg — Zilber map      122 247
Eilenberg — Zilber theorem      122 167
Elementary spectral sequence      86
Elliptic homology      500
Equivariant cohomology      501
Equivariant homology      340
Equivariant Leray — Serre spectral sequence      502
Euler characteristic      14
Exact couple      37ff.
Excess      196
Exhaustive filtration      62
Ext      376ff.
Extended module      237
Extension condition      105
Extension problem      32
Exterior algebra      20 124
Face map      103
Federer spectral sequence      490
Fiat module      53
Fibrant simplicial set      357
Fibration      109
Fibration spectral sequence constructor      229
Fibre      110
Fibre bundle      208
Filtered differential graded module      33
Filtration      31
Filtration degree      4
Filtration topology      87
Filtration, bounded      3 33
Filtration, decreasing/increasing      31
Filtration-preserving action      17
Finite CW-complex      94
Finite H-space      476
Finite type      159
Finiteness of $\pi_{2n+k} (S^{2n-1})$      162
First derived functor of lim      69
First Eilenberg — Moore theorem      241
Five-lemma      26
Five-term exact sequence      6
Formal space      310
Framed manifold      409
Free and proper group action      337
Free graded commutative algebra      258
Free loop space      178
Free path space      110
Freudenthal suspension theorem      99 192
Frobenius homomorphism      215 475
Froelicher spectral sequence      518
Functional cup product      367
Fundamental group, action of      330ff.
Fundamental groupoid      164
Generalized (co)homology theory      495
Generalized sheaf cohomology groups      520
Geometric cobar construction      322
Geometric realization of a simplicial set      107
Graded algebra      10
Graded commutative bigraded algebra      24
Graded commutativity      20
Grassmann manifold      207
Grothendieck spectral sequence      514
Grouplike space      481
Gysin sequence      8 143
H-space      125
Hausdorff filtration      64
Height      213
Hidden extension      450
Higher order Bockstein operator      460
Higher order cohomology operations      371
Higher order linking invariants      304
Hirsch formulas      288
history      133 207 222
Hochschild homology      509
Hochschild-Serre spectral sequence      511
Hodge-de Rham spectral sequence      517
Holes      8
Hom-tensor interchange      376
Homogeneous spaces      113 212 274ff.
Homological perturbation theory      224
Homology Eilenberg — Moore spectral sequence      268
Homology of a group      335
Homology of an algebra      378
Homology suspension      190
Homology with local coefficients      166
Homotopy colimit      503
Homotopy extension property (HEP)      96
Homotopy groups of a Kan complex      106
Homotopy lifting property (HLP)      109
Homotopy limit      503
Hopf algebra      125
Hopf algebra extension      513
Hopf fibration      113
Hopf invariant      366
Hopf map      366
Hopf — Borel theorem      213
Hurewicz fibration      109
Hurewicz spectral sequence      490
Hurewicz Theorem      108 157
Hurewicz-Serre theorem      205
Hypercohomology spectral sequence      514
Hyperderived functor      514
Image computing spectral sequence      506
Implications      469
Important observation      6
Incidence number      100
Indecomposable      125
Infinite loop space      499
Injective comodule      271
Injective module      377
Integers localized at a prime      354
Inverse limit      67
J-homomorphism      450
Jacobi identity      303 347
Joke, booty boot hog      558
Juxtaposition product      382
K-invariant      121
Kan complex      105
Kervaire invariant      451
Koszul complex      259
Koszul resolution      260
Kudo transgression theorem      192
Kuenneth spectral sequence      56
Kuenneth theorem      45
Kuenneth theorem for Top/B      315
Lambda-algebra      493
Leibniz algebra      512
Leibniz cohomology      512
Lens space      132 198
Leray spectral sequence      515
Leray — Hirsch theorem      148
Leray — Serre spectral sequence for generalized theories      498
Lifting function      110
LIMIT      67
Local ring      310
Local-to-global spectral sequence      515
Locally finite CW-complex      94
Locally finite module      14
Locally trivial fibration      112
Loop multiplication      98
Loop suspension homomorphism      298
Lower central series      343 345
Lucas's Lemma      263
Lusternik — Schnirelmann category      302 347
Lyndon — Hochshild — Serre spectral sequence      340ff.
Mapping cone      97
Mapping cylinder      97
Massey products in Ext      426ff.
Massey products, n-fold      305
Massey triple product      302
Matching space      358
MathSciNet      488
Matric Massey products      311ff.
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