scholarly journals Subspace arrangements and property T

2011 ◽  
pp. 445-477 ◽  
Author(s):  
Martin Kassabov
Keyword(s):  
Subspace Arrangements ◽  
Property T

scholarly journals Local rigidity for actions of Kazhdan groups on noncommutative Lp-spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550064
Author(s):  
Bachir Bekka
Keyword(s):  
Von Neumann Algebra ◽  
Regular Representation ◽  
Von Neumann ◽  
Lp Spaces ◽  
Local Rigidity ◽  
Left Regular Representation ◽  
Left Regular ◽  
Property T ◽  
Finite Factor ◽  
Finite Index Subgroup

Let Γ be a discrete group and 𝒩 a finite factor, and assume that both have Kazhdan's Property (T). For p ∈ [1, +∞), p ≠ 2, let π : Γ →O(Lp(𝒩)) be a homomorphism to the group O(Lp(𝒩)) of linear bijective isometries of the Lp-space of 𝒩. There are two actions πl and πr of a finite index subgroup Γ+ of Γ by automorphisms of 𝒩 associated to π and given by πl(g)x = (π(g) 1)*π(g)(x) and πr(g)x = π(g)(x)(π(g) 1)* for g ∈ Γ+ and x ∈ 𝒩. Assume that πl and πr are ergodic. We prove that π is locally rigid, that is, the orbit of π under O(Lp(𝒩)) is open in Hom (Γ, O(Lp(𝒩))). As a corollary, we obtain that, if moreover Γ is an ICC group, then the embedding g ↦ Ad (λ(g)) is locally rigid in O(Lp(𝒩(Γ))), where 𝒩(Γ) is the von Neumann algebra generated by the left regular representation λ of Γ.

On property (T) for Aut(Fn) and SLn(ℤ)

2021 ◽  
Vol 193 (2) ◽  
pp. 539
Author(s):  
Kaluba ◽  
Kielak ◽  
Nowak
Keyword(s):  
Property T

Property (T)

2016 ◽  
pp. 131-146
Author(s):  
David Kerr ◽  
Hanfeng Li
Keyword(s):  
Property T

scholarly journals Dynamical properties of profinite actions

2011 ◽  
Vol 32 (6) ◽  
pp. 1805-1835 ◽  
Author(s):  
MIKLÓS ABÉRT ◽  
GÁBOR ELEK
Keyword(s):  
Finite Index ◽  
Linear Groups ◽  
Regular Graphs ◽  
Weak Containment ◽  
Residually Finite Groups ◽  
The Family ◽  
Property T ◽  
Free Actions ◽  
Theoretical Consequence ◽  
Lattice Of Subgroups

AbstractWe study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic. This allows us to construct continuum many pairwise weakly inequivalent free actions of a large class of groups, including free groups and linear groups with property (T). We also prove that for chains of subgroups of finite index, Lubotzky’s property (τ) is inherited when taking the intersection with a fixed subgroup of finite index. That this is not true for families of subgroups in general leads to the question of Lubotzky and Zuk: for families of subgroups, is property (τ) inherited by the lattice of subgroups generated by the family? On the other hand, we show that for families of normal subgroups of finite index, the above intersection property does hold. In fact, one can give explicit estimates on how the spectral gap changes when passing to the intersection. Our results also have an interesting graph theoretical consequence that does not use the language of groups. Namely, we show that an expanding covering tower of finite regular graphs is either bipartite or stays bounded away from being bipartite in the normalized edge distance.

scholarly journals ENDOMORPHISMS OF RELATIVELY HYPERBOLIC GROUPS

2008 ◽  
Vol 18 (01) ◽  
pp. 97-110 ◽  
Author(s):  
IGOR BELEGRADEK ◽  
ANDRZEJ SZCZEPAŃSKI
Keyword(s):  
Hyperbolic Group ◽  
Hyperbolic Groups ◽  
Parabolic Subgroups ◽  
Relatively Hyperbolic Groups ◽  
Property T ◽  
Relatively Hyperbolic Group ◽  
Finite Index Subgroup ◽  
Relatively Hyperbolic ◽  
Finitely Presented ◽  
Slender Group

We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. • If G is a nonelementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out (G) is infinite, then G splits over a slender group. • If H is a nonparabolic subgroup of a relatively hyperbolic group, and if any isometric H-action on an ℝ-tree is trivial, then H is Hopfian. • If G is a nonelementary relatively hyperbolic group whose peripheral subgroups are finitely generated, then G has a nonelementary relatively hyperbolic quotient that is Hopfian. • Any finitely presented group is isomorphic to a finite index subgroup of Out (H) for some group H with Kazhdan property (T). (This sharpens a result of Ollivier–Wise).

Sign in / Sign up

Export Citation Format

Share Document