Quasiconvex Subgroups and Nets in Hyperbolic Groups
Geometric Topology
2007-05-23 v2 Group Theory
Abstract
Consider a hyperbolic group G and a quasiconvex subgroup H of infinite index. We construct a set-theoretic section s of the quotient map (of sets) from G to G/H such that s(G/H) is a net in G; that is, any element of G is a bounded distance from s(G/H). This section arises naturally as a set of points minimizing word-length in each fixed coset gH. The left action of G on G/H induces an action on s(G/H), which we use to prove that H contains no infinite subgroups normal in G.
Cite
@article{arxiv.math/0608212,
title = {Quasiconvex Subgroups and Nets in Hyperbolic Groups},
author = {Thomas Mack},
journal= {arXiv preprint arXiv:math/0608212},
year = {2007}
}
Comments
15 pages, 1 figure; v3: Replaced another typo; v2: Replaced minor typo in abstract