Quantifying separability in virtually special groups
Pacific Journal of Mathematics
Mathematical Society Publishing
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Hagen, M., & Patel, P. (2016). Quantifying separability in virtually special groups. Pacific Journal of Mathematics https://www.repository.cam.ac.uk/handle/1810/254203
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.
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.
This record's URL: https://www.repository.cam.ac.uk/handle/1810/254203