Monod N. — Continuous Bounded Cohomology of Locally Compact Groups :: Электронная библиотека попечительского совета мехмата МГУ

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Monod N. — Continuous Bounded Cohomology of Locally Compact Groups

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Название: Continuous Bounded Cohomology of Locally Compact Groups

Автор: Monod N.

Аннотация:

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on TeichmA1/4ller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2001

Количество страниц: 214

Добавлена в каталог: 23.11.2009

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Предметный указатель

$Alt_{n}$       77
$B^{n}(G,E)$       62
$C^{n}_{b}(G,E)$       61
$C_{b}$       17
$C_{ub}$       46
$D^{n}$       62
$EH^{n}_{cb}(G,E)$ , $EH^{n}_{b}(G,E)$       122
$E^{G}$       15
$E^{\flat}$       13
$E^{\sharp}$       13
$G^{0}$       148
$G^{op}$       12
$H^{n}(E^{\bullet})$       69
$H^{n}_{b}(\Gamma,E)$       62
$H^{n}_{b}(\Gamma,Z)$       63
$H^{n}_{cb}(G,E)$       62
$H^{n}_{cb}(G,\alpha)$       91
$H^{n}_{cb}(\psi,E)$       101
$H^{n}_{cb}(\psi,\alpha)$       102
$H^{n}_{c}(G,A)$       120
$I^{G}_{H}E$       130
$i^{n}_{S}$       131
$K_{G}(H)$       113
$L^{p}$ induction map      138
$L^{p}$ induction module      137
$L^{p}i$       138
$L^{p}I^{G}_{H}E$       137
$L^{[p]}$       136
$L^{\infty}$ homogeneous resolution      83
$L^{\infty}$ inhomogeneous complex      90
$L^{\infty}$ spaces      19
$L^{\infty}_{w^{*},alt}$       82
$L^{\infty}_{w^{*}}$       19
$Mod(\Sigma)$       184
$Teich(\Sigma)$       184
$Z^{n}(G,E)$       62
$Z_{G}(H)$       100
$\delta_{\pi}$       81
$\ell^{\infty}(X,E)$       23
$\epsilon$       49
$\int^{(B)}$       25
$\int^{(GD)}$       26
$\lambda$       17 19
$\lambda_{\pi}$       17 19
$\mathcal{C}$       14
$\mathcal{C}_{\pi}$       15
$\mathcal{L}$       9 13
$\mathcal{S}_{n}$       77
$\mathfrak{S}E$ , $\mathfrak{S}^{k}E$       141
$\mathfrak{S}_{S}E$ , $\mathfrak{S}^{k}_{S}E$       142
$\mathfrak{X}^{Hilb}$ , $\mathfrak{X}^{refl}$ , $\mathfrak{X}^{cont}$       144
$\partial^{n}$       61
$\Psi^{n}$ , $\Psi^{n}_{G}$       122
$\underline{E}^{\bullet}$       67
$\varrho$       21
$\widehat{\otimes}$       14
$^{I}E^{\bullet,\bullet}_{\bullet}$ , $^{II}E^{\bullet,\bullet}_{\bullet}$       158
a(G)      148
Action on the circle      182
Adjoint morphism      13
Admissibility of the coefficient inclusion      54
Admissible morphism      32
Alternating      77
Amenable action      48
Amenable G-space      48
Amenable group      45 46
Amenable in the sense of Eymard      105
Amenable space      48
Approximate identity      27
Augmentation      69
Augmented resolution      69
Augmented strong resolution      70
Baire space      10
Banach G-module      9
Bochner integration      24
Bochner's integral      24
Bounded cohomology      62
Bounded Euler class      182
Bruhat function      39 40
Canonical augmented resolution      62
Canonical complex      62
Characterization of amenable action      58
co-Folner      105
Coboundary      62
Coboundary map      67
Cochain      67
Cocycle      62
Coefficient G-module      13
Coefficient inclusion      49
Coefficient module      13
Coefficient representation      100
Cohen's factorization theorem      28
Comparison map      122
COMPLEX      67
Conditional expectation      49
Conjugation action on cohomology      111 114
Continuous action (modules)      10
Continuous action (spaces)      17
Continuous Banach G-module      10
Continuous bounded cohomology      62
Continuous cohomology      120
Continuous G-R module      121
Continuous homogeneous resolution      63 80
Continuous inhomogeneous complex      82 121
Continuous rough action      171
Contracting homotopy      68
Contragredient      13
Contragredient Banach G-module      13
Curve complex      184
Degenerate representation      193
Degree      67
Differential      67
Dimension shifting      141
Disintegration      52
Double $\mathfrak{X}$ -ergodicity      144
Dunford — Pettis theorem      20
Dupont isomorphism      126
Eckmann — Shapiro Lemma      129
Eilenberg — MacLane cohomology      120
Equivariant mean      49
Equivariant vs. invariant      15 17

Etalee      52
Extension problem      32
Extension to a complex      71
g*      148
G-homologism      69
G-homotopic      68
G-homotopy      68
G-homotopy equivalence      68
G-morphism      9
G-morphism of complexes      67
G-split      35
G-split exact sequence      35
Gelfand — Dunford integral      26
Gelfand — Dunford integration      26
Gelfand — Dunford theorem      26
Generalized extension problem      36
Generic group      175
Gromov's semi-norm      119 169
Hochschild — Serre spectral sequence      157
Hochschild — Serre spectral sequence for discrete groups      167
Homogeneous differential      62 77
Homogeneous resolution      77
Homogeneous resolution on amenable spaces      83
Homologism      69
Homotopic      68
Homotopy      67
Homotopy equivalence      68
i      131
Induction map      131
Induction module      130
inf      103
Inflation      88 103
Inhomogeneous differential      81
Injective (relatively)      32
Integral bounded cohomology      63
Integration      24
Invariant mean      45
Irreducible lattice      186
Kazhdan's property (T)      173
Left regular representation      17 19
Left translation      17 19
LHS exact sequence      163
LHS exact sequence for discrete groups      166
Local map      49
Mapping class group      184
Mautner's property      129 147
Maximal continuous Banach G-module      14
Maximal continuous submodule      14
Mazur — Ulam theorem      170
Mean      49
Measure-theoretic quotient      53
Michael's selection theorem      93
Morphism of Banach spaces      9
Morphism of coefficient modules      13
Morphism of complexes      67
Morphism of topological groups      101
Non elementary lattice      187
Non elementary subgroup      188
Null homotopic      68
Opposite group      12
Over S shifting module      142
Paracompact      40
Paracompact quotient      44
Paracompact space      40
Perturbed action      171
Point realization      53
Poisson boundary      18 52
Poisson transform      87
Positive linear map      49
Proper action      39
Proper G-space      39
Proper map      40
Proper space      39
Property (T)      173
Property (TT)      173
QM(G), $QM_{c}(G)$       176
Quasi-isomorphism      69
Quasi-morphism      176
Quotient (measure-theoretic)      53
Reducible lattice      186
Regular G-space      18
Regular space      18
Relative injectivity      32
Relatively injective Banach G-module      32
Relatively injective module      32
res      105
Resolution      69
Restriction      105
Right Banach G-module      12
Right complex      67
Right translation      21
Rough action      170
Ryll-Nardzewski theorem      65
Schreier graph      150
Semi-conjugated      182
Semi-continuous rough action      171
Shifting (over S) module      142
Shifting module      141
SIGN      77
Spectral sequence      157
Spectral sequence for discrete groups      167
Stable length      176
Strict approximate identity      27
Strong augmented resolution      70
Strong complex      68
Strong resolution      70
Sub-additivity      25
Teichmueller space      184
Tensor product of Banach G-module      14
Thurston's stability theorem      183
Topological G-R module      120
Topological LHS exact sequence      168
Topological module      120
TRANSFER      105
Transgression map      93 97
Trivial Banach G-module      9
Uniformly bounded representation      12
van Est theorem      121
Weak-* measurable      19
Weakly admissible exact sequence      34
Weakly admissible morphism      34
Z(H)      100

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