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Volume vs. Complexity of Hyperbolic Groups

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 نشر من قبل Nir Lazarovich
 تاريخ النشر 2021
  مجال البحث
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 تأليف Nir Lazarovich




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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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