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Cheeger constant and algebraic entropy of linear groups

Emmanuel Breuillard·Tsachik Gelander
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Abstract

We prove a uniform version of the Tits alternative. As a consequence, we obtain uniform lower bounds for the Cheeger constant of Cayley grahs of finitely generated non virtually solvable linear groups in arbitrary characteristic. Also we show that the algebraic entropy of discrete subgroups of a given Lie group is uniformly bounded away from zero.

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Emmanuel Breuillard, Tsachik Gelander. 2005-07-21. Cheeger constant and algebraic entropy of linear groups. https://arxiv.org/abs/math/0507441

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