Groups acting on quasiconvex spaces and translation numbers

Poleksić, Aleksandar

doi:10.1090/S0002-9939-00-05537-4

Groups acting on quasiconvex spaces and translation numbers
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Proc. Amer. Math. Soc. 128 (2000), 3177-3183 Request permission

Abstract:

We prove that groups acting geometrically on $\delta$-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.

References

Juan M. Alonso and Martin R. Bridson, Semihyperbolic groups, Proc. London Math. Soc. (3) 70 (1995), no. 1, 56–114. MR 1300841, DOI 10.1112/plms/s3-70.1.56
G. Conner, Translation numbers of groups acting on convex spaces, Brigham Young University, preprint (1994).
S. M. Gersten and H. B. Short, Rational subgroups of biautomatic groups, Ann. of Math. (2) 134 (1991), no. 1, 125–158. MR 1114609, DOI 10.2307/2944334
E. Ghys and P. de la Harpe, Infinite groups as geometric objects (after Gromov), Chapter 10 of Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces (T. Bedford, M. Keane, and C. Series, Eds.), Oxford Univ. Press (1991), 299-314.
M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
A. Poleksic, Translation numbers in negatively curved groups, Topol. and its Appl., to appear.
A. Poleksic, The boundary of a quasiconvex space, Topol. and its Appl., to appear.