Quasiconvex Subgroups and Nets in Hyperbolic Groups

Details Quasiconvex Subgroups and Nets in Hyperbolic Groups Quasiconvex Subgroups and Nets in Hyperbolic Groups

2006-08-09

arxiv.org/abs/math/0608212v2

Mathematics

Geometric Topology

15 pages, 1 figure; v3: Replaced another typo; v2: Replaced minor typo in abstract

Scientific paper

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.

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