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 less than $\varepsilon$?
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1$\begingroup$ It seems so, by Gelander and Zuk ams.org/mathscinet/search/… $\endgroup$– Dan SălăjanNov 20, 2013 at 8:31
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$\begingroup$ Yes, "most" higher rank lattices have this property. $\endgroup$– MishaNov 20, 2013 at 13:52
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$\begingroup$ @Dan: thanks - can you give this comment as an answer so that I can accept it? $\endgroup$– Michal KotowskiNov 20, 2013 at 14:22
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1 Answer
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The answer is yes, by Gelander and Zuk: http://www.ams.org/mathscinet/search/publdoc.html?pg1=INDI&s1=697297&vfpref=html&r=24&mx-pid=1910934
