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Volume vs. Complexity of Hyperbolic Groups

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arxiv 2107.13250 v1 pith:P4OP7MMR submitted 2021-07-28 math.GR math.GT

Nir Lazarovich This is my paper · ORCID
classification math.GRmath.GT
keywords hyperbolicgroupsone-endedactingapplybelowboundscannot
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abstract

We prove that for a one-ended hyperbolic graph $X$, the size of the quotient $X/G$ by a group $G$ acting freely and cocompactly bounds from below the number of simplices in an Eilenberg-MacLane space for $G$. We apply this theorem to show that one-ended hyperbolic cubulated groups (or more generally, one-ended hyperbolic groups with globally stable cylinders \`a la Rips-Sela) cannot contain isomorphic finite-index subgroups of different indices.

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Cited by 1 Pith paper

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  1. Stable cylinders and fine structures for hyperbolic groups and curve graphs

    math.GT 2025-01 conditional novelty 8.0 of 10

    Every residually finite hyperbolic group, and every curve graph of a finite-type surface, admits globally stable cylinders.

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