The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups

Details The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups

2002-01-10

arxiv.org/abs/math/0201076v3

Mathematics

Group Theory

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Scientific paper

We show that if $H$ is a quasiconvex subgroup of infinite index in a
non-elementary hyperbolic group $G$ then the Schreier coset graph $X$ for $G$
relative to $H$ is non-amenable (that is, $X$ has positive Cheeger constant).
We present some corollaries regading the Martin boundary and Martin
compactification of $X$ and the co-growth of $H$ in $G$.

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