Quasiconvexity and Amalgams

1995/06/27 by Ilya Kapovich, Kapovich, Ilya
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR

paper · pdf · doi:10.48550/arxiv.math/9506206

AMS-Tex, 28 pages, no figures. Submitted to Intern. J. Alg. Comp

arxiv created 1995/06/27 · openalex publication_date 1995/06/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that is such that all their finitely generated subgroups are quasiconvex. It is known that free groups, hyperbolic surface groups and most 3-dimensional Kleinian groups have property (Q). We also give some applications of our results to one-relator groups and exponential groups.

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