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

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Hovey M., Palmieri J.H., Strickland N.P. — Axiomatic stable homotopy theory
Hovey M., Palmieri J.H., Strickland N.P. — Axiomatic stable homotopy theory

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Axiomatic stable homotopy theory

Авторы: Hovey M., Palmieri J.H., Strickland N.P.

Аннотация:

This book gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a "stable homotopy category"; using these axioms, one can make various constructions — cellular towers, Bousfield localization, and Brown representability, to name a few. Much of the book is devoted to these constructions and to the study of the global structure of stable homotopy categories.
Next, a number of examples of such categories are presented. Some of these arise in topology (the ordinary stable homotopy category of spectra, categories of equivariant spectra, and Bousfield localizations of these), and others in algebra (coming from the representation theory of groups or of Lie algebras, as well as the derived category of a commutative ring). Hence one can apply many of the tools of stable homotopy theory to these algebraic situations.

Features:

Provides a reference for standard results and constructions in stable homotopy theory.

Discusses applications of those results to algebraic settings, such as group theory and commutative algebra.

Provides a unified treatment of several different situations in stable homotopy, including equivariant stable homotopy and localizations of the stable homotopy category.

Provides a context for nilpotence and thick subcategory theorems, such as the nilpotence theorem of Devinatz-Hopkins-Smith and the thick subcategory theorem of Hopkins-Smith in stable homotopy theory, and the thick subcategory theorem of Benson-Carlson-Rickard in representation theory.

This book presents stable homotopy theory as a branch of mathematics in its own right with applications in other fields of mathematics. It is a first step toward making stable homotopy theory a tool useful in many disciplines of mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 114

Добавлена в каталог: 15.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$c(\mathcal{C})$      21 54
$coloc\langle\mathcal{S}\rangle$      10
$E(R/\mathfrak{p})$      67
$G\mathcal{S}^{U}$      86
$H_{X}$      46 53
$I_{\mathfrak{p}}$      68
$K(\mathfrak{p})$      68—71
$k_{Z}$      77
$loc(\mathcal{S})$      10
$L^{f}_{B}$      95
$L_{<\mathfrak{p}}$      68
$L_{\mathfrak{p}}$      67 68
$M_{\mathfrak{p}}$      66—69 71
$M_{\mathfrak{p}}^{\diamond}$      66 67
$M_{\mathfrak{p}}^{\wedge}$      66 67
$S/\mathfrak{p}$      68
$S^{k}$      9
$S_{\mathfrak{p}}$      67
$S_{\mathfrak{p}}^{\diamond}$      68 74
$t_{B}(M)$      95
$U_{*}$, $U^{*}$      55
$U_{f}$      61
$V_{*}$, $V^{*}$      55 59 60
$x\wedge y$      4
$x^{(n)}$      62
$X^{(\infty)}$      62
$\Lambda(X)$      22 58
$\Lambda_{\mathcal{A}}(X)$      22
$\langle X\rangle$      45—47 49 50 63
$\mathcal{C}(B)$      69 77 88 94 95 97
$\mathcal{C}^{C}$      28
$\mathcal{C}_{*}$, $\mathcal{C}^{*}$      55 59 60
$\mathcal{C}_{L}$      28 40 41 43 44 46
$\mathcal{C}_{\kappa}$      21
$\mathcal{C}_{\mathfrak{p}}$      67
$\mathcal{F}_{*}$, $\mathcal{F}^{*}$      55
$\mathcal{G}$-coideal      9 10
$\mathcal{G}$-finite      24
$\mathcal{G}$-ideal      9 10 12 21
$\mathcal{G}$-Mod      78
$\mathcal{G}$-module      78
$\mathcal{K}(B)$      87
$\mathcal{M}_{\mathfrak{p}}$      68 70 72
$\mathcal{P}(X,Y)$      55
$\mathcal{S}$-finite      12
$\mathcal{S}^{\mathcal{U}}_{G}$      87
$\overline{h}G\mathcal{S}^{U}$      86 87
$\overline{k(\mathfrak{p})}$      69
$\pi_{K}$      9
$\underline{Hom}_{B}(M,N)$      94
$\widehat{H}$      22 24
$\widehat{H}_{\mathcal{A}}$      22 25 26
$\widehat{\pi}$      9 46 53
Acyclic      28 34 45
Adams spectral sequence      99
Additive category      6
Additive category, enriched      81
algebraic      5
Algebraic localization      39 67
Bounded below      76
Bousfield class      45—47 49 50 63
Bousfield class, generalized      45
Bousfield equivalent      45
Bousfield lattice      45 74
Brown category      5 41 53 54 56 58—61
C(X)      21
Cardinality      21
Cellular approximation      79
Cellular tower      20 21 26 76
Chain complex      80
Chain homotopy      81
Closed model category      3 15—17 34 35 79 83 87 94
Closed symmetric monoidal category      104
Closed under specialization      69 72
Cocomplete      10
Cofiber      102 103
Cofinal functor      22
Cofree      90
Cohomology functor      4
Cohomology functor, graded      9
Cohomology functor, representable      4
Coideal      9
Coideal, colocalizing      9
Coideal, colocalizing, closed      45
Colimit, homotopy      16
Colimit, minimal weak      14 56 58
Colimit, sequential      15 16
Colimit, weak      14 15
Colocal      28
Colocalization, functor      28 29
Colocalizing, coideal      9
Colocalizing, subcategory      9
Comod(B)      87 93
Comodule      7
Comodule, cofree      90
Comodule, extended      90
Comodule, injective      90
complete      10 85
Connective      75
Derived category      7 40 54 66 69 83
Detect nilpotence      63 71
Determine $\mathcal{G}$-ideals      65
Division algebra      77
Eilenberg swindle      11
Eilenberg — MacLane object      76
Enriched      6 20 81
EQUIVALENCE      28
Essentially small      9 21
Exact functor      4 103
Exact triangle      102
Extended      90
F(X,Y)      4
f-phantom      55
F-small      12
Fiber      103
Field object      48
Field object, skew      48
Filtered category      22 24 25 56
Finite localization      36 39 43 95
G-map      85
G-space      85
G-spectrum      85
GENERATED      9
Generators      5
Geometric morphism      39 40 79
Geometric morphism, lax      39
Grading system      100
Heart      76
Homology functor      4
Homology functor, graded      9
Homology functor, representable      53
Homotopy colimit      16
Homotopy group      9
Hopf algebra      7 66 87 88 94 95 97 99
Ideal      9
Ideal, localizing      9
Ideal, localizing, closed      45
Idempotent      11
Infective comodule      93
Injective hull      67
Inverse limit      25
Invertible      108
Isotropy ($\mathcal{U}$)      85 86
Koszul algebra      94
Lax      39
Lie group      7 85
Limit, sequential      18
Limit, weak      18
Lindner category      101
Linear topology      24 61
Linearly compact      24 25
local      28 34 45
localization      8 40 43 44
Localization at a prime ideal      67
Localization with respect to homology      34
Localization, algebraic      39 67
Localization, away from      36 39
Localization, finite      36 39 43 52 95
Localization, functor      27 29 34
Localization, smashing      35 41 50 59 60 75
Localizing      9
Localizing, ideal      9
Localizing, subcategory      4 26 74
Mackey functor      101
Max R      66
Minimal weak colimit      14 56 58
Module object      48
Monochromatic category      68
Monogenic      5 8 10 75
Monoidal      46 63
Morava K-theory      8
Multigraded      8 77
Natural topology      61
Nilpotence      71
Nilpotence theorem      62 99
Nilpotent      62 63 98
Noetherian      66 67 71 88
Octahedral axiom      19 58 102
Ordinary homology      76
Phantom      55 58 59 61
Picard category      100 108
Picard group      100 108
Postnikov tower      76
Prespectrum      85
Quasi-isomorphism      82
Replete      44
Representable      4 53 54 62
Ring object      48 63
Semisimple      77 78
Sequential colimit      15—17 64
Sequential limit      18
Simple comodule      88 90 93
Small      4 12 24 26
Smash nilpotent      63
Smash-complemented      48
Smashing      35 41 50 59 60 7
Spanier — Whitehead dual      107
Spec R      66 69
Spectrum      85
Stable homotopy category      5
Stable homotopy category, $\mathcal{J}$-graded      100
Stable homotopy category, algebraic      5
Stable homotopy category, connective      75
Stable homotopy category, monogenic      5
Stable homotopy category, Noetherian      66 67 71
Stable homotopy category, product      78
Stable homotopy category, semisimple      77 78
Stable homotopy category, unital algebraic      5
Stable morphism      40 83 88
Stable morphism, lax      40
StComod(B)      94 97
Strongly dualizable      4 12 107
Subcategory, colocalizing      9
Subcategory, localizing      4 9 26 74
Subcategory, thick      9 21
supp(X)      69
Support      65
Suspension      102
Symmetric monoidal category, pointed      100
t-structure      76
Tame      88
Tate cohomology      97
Tate complex      95
Telescope      15 16 47 64
Telescope conjecture      39 69 74 75
thick ($\mathcal{S}$)      10
Thick subcategory      9 21 72 94 97
Thick subcategory theorem      62 65 69
Triangulated category      103
Triangulated category, cocompiete      10
Triangulated category, complete      10
Triangulated category, enriched      6 20 79 81
Triangulation      102
Unital algebraic      5
Universe      85
Universe, complete      85
Universe, incomplete      87
Weak colimit      14 15
Weak limit      18
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте