Topology & Geometric Group Theory Seminar

Fall 2007

2:55 - 3:55, Malott 310D

Tuesday, October 16

Uzy Hadad, Hebrew University

Uniform Kazhdan Constant for some families of linear groups

Let R be a ring generated by l elements with stable range r. Assume that the group ELd(R) has Kazhdan constant ε0 > 0 for some d ≥ r+1. We prove that there exist ε(ε0, l) > 0 and k in N, such that for every n ≥ d, ELn(R) has a generating set of order k and a Kazhdan constant larger than ε. As a consequence, we obtain for SLn(Z) where n ≥ 3, a Kazhdan constant which is independent of n with respect to generating sets of a fixed size.

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