caa a22 4500 445884444 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9492-9 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9492-9 Zuddas Fabio Dipartimento di Matematica, Università di Parma, Parma, Italy aut A finiteness result for groups which quasi-act on hyperbolic spaces [Elektronische Daten] [Fabio Zuddas] Let (X, d) be a Gromov-hyperbolic metric space endowed with a measure having finite entropy H and such that the measure of every ball of radius R>0 is finite and bounded from below by a positive function of R. In this paper we look at the set Q(X; L, C, D) of the isomorphism classes of torsion-free groups Γ which admit a discrete, D-co-bounded (L, C)-quasi-action on X (D >0, L ≥ 1, C ≥ 0) and we describe some algebraic conditions which, imposed on the groups Γ, define finite subsets of Q(X; L, C, D), provided C < ε for some ε >0. As an example, these conditions are satisfied when Γ is assumed to admit a faithful, discrete, m-dimensional representation over some local field (in this case ε = ε(m, H, L)). In particular (set C=0, L=1), our results apply when the groups are assumed to act by isometries. Springer Science+Business Media B.V., 2010 Gromov-hyperbolic space nationallicence Word-hyperbolic group nationallicence Quasi-action nationallicence Quasi-isometry nationallicence Entropy nationallicence Finiteness result nationallicence Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 35-47 0046-5755 150:1<35 2011 150 10711 https://doi.org/10.1007/s10711-010-9492-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9492-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zuddas Fabio Dipartimento di Matematica, Università di Parma, Parma, Italy aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 35-47 0046-5755 150:1<35 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer