Translation numbers of groups acting on quasiconvex spaces [chapter]

Gregory R. Conner, Michael Atkinson, Nick Gilbert, James Howie, Steve Linton, Edmund Robertson
Computational and Geometric Aspects of Modern Algebra  
We define a group to be translation discrete if it carries a metric in which the translation numbers of the non-torsion elements are bounded away from zero. We define the notion of quasiconvex space which generalizes the notion of both CAT(0) and Gromov-hyperbolic spaces. We show that a cocompact group of isometries acting properly discontinuously cocompactly on a proper quasiconvex metric space is translation discrete if and only if it does not contain an essential Baumslag-Solitar quotient.
more » ... follows that if such a group is either biautomatic or residually finite then it is translation discrete.
doi:10.1017/cbo9780511600609.003 fatcat:7ujzzi7onvdbzazypvnvnaxwpq