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Quantifying separability in virtually special groups

Accepted version
Peer-reviewed

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Authors

Hagen, MF 
Patel, P 

Abstract

We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if G is a virtually compact special hyperbolic group, and Q ≤ G is a K-quasiconvex subgroup, then any g ∈ G − Q of word-length at most n is separated from Q by a subgroup whose index is polynomial in n and exponential in K. This generalizes a result of Bou-Rabee and the authors on residual fi niteness growth and a result of the second author on surface groups.

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Keywords

subgroup separable, right-angled Artin groups, quantifying, virtually special groups

Journal Title

Pacific Journal of Mathematics

Conference Name

Journal ISSN

0030-8730
0030-8730

Volume Title

Publisher

Mathematical Sciences Publishers
Sponsorship
The authors acknowledge travel support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: Geometric Structures and Representation Varieties" (the GEAR Network) and from grant NSF 1045119. M.F.H. was supported by the National Science Foundation under Grant Number NSF 1045119.