Questions tagged [property-t]

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Kazhdan Property T of semisimple Lie groups

I am reading the paper [Margulis, G. A.; Nevo, A.; Stein, E. M., Analogs of Wiener's ergodic theorems for semisimple Lie groups. II. Duke Math. J. 103 (2000), no. 2, 233–259] (MSN). I want to ...
3
votes
0answers
150 views

Property (T) for pairs

I was reading the excellent book by Bekka, de la Harpe, and Valette (link at Bekka's page), and on its list of open questions I was looking at p300 Question 7.7: $L\subset K\subset H\subset G$.$H,K,...
3
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0answers
65 views

Relative property (T) and normal closure

I am in a situation where a discrete, finitely generated group $H$ satisfies property (T), and was wondering if I was able to conclude anything about the pair $(G,H^G)$, where $G$ is a finitely ...
13
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0answers
416 views

On uniform Kazhdan's property (T)

For a finitely generated group $\Gamma$ and its finite generating subset $S$, the Kazhdan constant $\kappa(\Gamma,S)$ is defined to be $$\kappa(\Gamma,S)=\inf_{\pi,v} \max_{g\in S} \| v - \pi_g v \|,$...
4
votes
1answer
297 views

Is there a one relator group with property (T)?

Is there an $n > 2$, and some $x \in F_n$ (the free group on $n$ generators) such that the quotient of $F_n$ by the normal subgroup generated by $x$ has Kazhdan's property $\mathrm{(T)}$ ?
5
votes
1answer
251 views

Do discrete groups with property $(T)$ have “modest” subgroup growth?

I saw it conjectured at http://www.mathunion.org/ICM/ICM1994.1/Main/icm1994.1.0309.0317.ocr.pdf that "discrete subgroups with property $(T)$ may have modest subgroup growth." (Page 5, directly above ...
13
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0answers
439 views

Does anybody know if the Fourier algebra of SL(3,Z) has an approximate identity?

(Note to those who like to tidy LaTeX, or ${\rm \LaTeX}$: I kindly request that you don't put any LaTeX in the title of this question, nor change the bolds below to blackboard bold.)$\newcommand{\FA}{{...
3
votes
1answer
208 views

Uniform bounds on Kazhdan constants in groups

Does there exist a finitely generated discrete group $G$ such that it has property (T), but for every $\varepsilon > 0$ there exists a generating set $S$ with the corresponding Kazhdan constant ...