Propagating quasiconvexity from fibers

2020/09/24 by Mj, Mahan, Sardar, Pranab
#20F65 #20F67 (Primary) #30F60(Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2009.11521

Abstract

Let 1 → K \longrightarrow G \stackrelπ\longrightarrow Q be an exact sequence of hyperbolic groups. Let Q₁ < Q be a quasiconvex subgroup and let G₁=π^-1(Q₁). Under relatively mild conditions (e.g. if K is a closed surface group or a free group and Q is convex cocompact), we show that infinite index quasiconvex subgroups of G₁ are quasiconvex in G. Related results are proven for metric bundles, developable complexes of groups, and graphs of groups.

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