Mislin G., Valette A. — Proper group actions and the Baum-Connes conjecture :: Электронная библиотека попечительского совета мехмата МГУ

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Mislin G., Valette A. — Proper group actions and the Baum-Connes conjecture

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Название: Proper group actions and the Baum-Connes conjecture

Авторы: Mislin G., Valette A.

Аннотация:

This book contains a concise introduction to the techniques used to prove the Baum-Connes conjecture.
The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature.
The book is aimed at advanced graduate students and researchers in the area, leading to current research problems.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 131

Добавлена в каталог: 27.10.2010

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Предметный указатель

$0\epsilon SC$       61
$CoC[\pi]$       65
$C^{+}$ -algebra, maximal      33
$C^{+}$ -algebra, reduced      33 80
$C^{+}$ -algebra, simple      39
$E\mathfrak{F}$       7
$G-Mod_{\mathfrak{F}}$       14
$HS_{G}^{\mathfrak{F}in}$       18
$HS_{H,\mathbb{C}}$       18
$H\mathcal{ETH}$       45
$H\mathcal{TH}$       42
$K_{*}$ -amenable      35
$LH\mathcal{ETH}$       46
$LH\mathcal{TH}$       42
$l_{2}$ -Betti numbers      63
$Mod_{\mathfrak{F}}-G$       8
$R_{\mathbb{C}}^{\mathfrak{F}in}$       17
$SO\epsilon SC$       62
$\Gamma$ -Compact      80
$\hat{A}$ -genus      60
$\mathbb{C}[FC(G)]$       17
$\mathfrak{D_{F}}(G)$ -space      31
$\mathfrak{D_{F}}(G)$ -spectrum      32
$\mathfrak{D}(G)$ -spectrum, $K^{top}$       36
$\mathfrak{F}in$       16
$\mathfrak{F}in(G)$       16
$\mathfrak{GB}$       27
$\theta(G)$       37
$\Theta_{max}(G)$       38
$\underline{B}G$       19
$\underline{E}G$       6 7
Abstract elliptic operator      90
AC      63
Assembly map      37
Assembly map, analytic      37 80 92
Assembly map, partial      57
Atiyah — Hirzebruch spectral sequence      49
Atiyih’s $l_{2}$ -Index Theorem      57
BCC      37 55
BCPwC      45
Bredon cohomology of G-spaces      11
Bredon cohomology of groups      10
Bredon homology of G-spaces      15
Bredon homology of groups      14
BTC      66
CAT(0)      41
Chern character      29 52
Conjecture, Atiyah      63
Conjecture, Base Trace      66
Conjecture, Baum — Connes      37 55 80
Conjecture, Baum — Connes with coefficients      45
Conjecture, Coarse Baum — Connes      87
Conjecture, Embedding      65
Conjecture, Gromov — Lawson — Roeenberg      61 81
Conjecture, Idempotent      55
Conjecture, Kadison      55
Conjecture, Kaplanski Kadison      81
Conjecture, Kaplansky      55
Conjecture, Novikov      59 81
Conjecture, Projective Class Group      70
Conjecture, Strong Bass Trace      71
Conjecture, Strong Idempotent      55
Conjecture, Strong Novikov      59 118
Conjecture, Strong Trace      57
Conjecture, Strong Zero-In-The-Spectrum      62
Conjecture, subgroup closed      55
Conjecture, Trace      56
Conjecture, Weak Bass Trace      67
Conjecture, Zero Divisor      63
Conjecture, Zero-In-The-Spectrum      61
Descent homomorphism      100
Dirac-dual Dirac      60
Directed union of groups      33
EC      65
Edge homomorphism      50
FC(G)      17
G-CW-complex      5
G-CW-complex, cocompact      5
G-CW-complex, G-simple      13
G-equivalence, weak      5
G-space, cocompact      5
G-space, coinduced      4
G-space, induced      3
G-space, proper      4
G-space, universal proper      6
G-spaces, join      4
Geometric group      90
GLRC      61
Group with property T      42
Group, $K_{+}$ -amenable      35
Group, a-T-menable      41
Group, acyclic      43 47
Group, amenable      34 41 61 67 84
Group, Baumslag — Solitar      51
Group, binale      47
Group, braid      47
Group, CAT(O)      70

Group, Coxeter      43
Group, elementary amenable      63 70
Group, geometric      90
Group, geometrically finite      44
Group, Haken 3-manifold      43
Group, hyperbolic      60 70
Group, K-amenable      35 84
Group, knot      43
Group, left orderable      62
Group, mapping class      69
Group, one-relator      21 51
Group, p-good      48
Group, semi-hyperbolic      70
Group, strongly bolic      60
Group, surface      41
Group, Thompson’s      43 62
Group, virtually connected Lie      60
Group, Weyl      3 9
Haagerup Property      41
Higher $\hat{A}$ -genus      60
Higher index theorem      62
Higher signatures      59
Hirzebruch L-class      59
Hirzebruch signature theorem      59
Homology theory, reduced      27
Homology theory, unreduced      27
Homotopy groups of a spectrum      27
Homotopy groups, stable      27
Hurewicz homomorphism      30
Hurewicz pairing      29
IC      55
Index map      80
Index theorem      57
Index theorem, higher      62
Induction structure      36
K-group, algebraic      34
K-group, topological algebraic      33
K-homology, representable      28
Kaplansky trace      19
Kasparov KK-groups      37
Kasparov triple      90
Kazhdan’s Property T      42
KK-groups      37
Metrically proper      41
NC      59
Operatorially homotopic      91
Orbit category      7
PC      60
PCGC      70
Pontrjagin classes      59
Positive-definite      93
Projective functor      9
Proper $\Gamma$ -space      88
Proper G-CW complex      6
Proper G-space      4
Proper metrically      41
Properly supported      90
Rapid Decay Property      60
RD      60
Regular representation      34
Representable homology theory      28
SBTC      71
SIC      55
Signature      59
Signature, analytic      60
Singular part      19
SNC      59
Spectrum      27
Spectrum, $K^{top,G}$       36
Spectrum, $K^{top,G}_{max}$       38
Spectrum, Bott      28
Spectrum, Eilenberg Mac Lane      28
Spectrum, equivariant K-homology      36
Spectrum, sphere      27
STC      57
Suspension isomorphism      32
TC      56
Tensor product of functors      14
Trace      65
Trace, augmentation      66
Trace, faithful      56
Trace, Hattori — Stallings      17 65
Trace, Kaplansky      19 56 66
Trace, universal      65
Unbounded Kasparov module      113
Universal coefficient sequence      29
Universal Coefficient spectral sequence      12
Universal coefficient spectral sequence, $\Gamma$ -space      89
Universal space G      16
Universal trace      65
von Neumann algebra      61
WBTC      67
Weak, Base Conjecture      68
Weak, G-equivalence      5
Weak, homotopy equivalence      5
Weak, topology      5 6
Whitehead theorem      6
ZDC      63

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