Abstract
Given an isometric action of the fundamental group of a closed orientable surface on a δ-hyperbolic space, we find a standard generating set whose translation distances are bounded above in terms of the hyperbolicity constant δ, the genus of the surface, and the injectivity radius of the action, which we assume to be strictly positive.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barnard, J.: Ends of Word-Hyperbolic Three-Manifolds. Ph.D. Thesis, Univ. of California, Santa Barbara (2004)
Bonahon F.: Bouts des variétés hyperboliques de dimension 3. Ann. Math. 124, 71–158 (1986)
Bowditch, B.H.: One-ended subgroups of mapping class groups. Preprint (2007). http://www.warwick.ac.uk/~masgak/
Bowditch B.H.: Atoroidal surface bundles over surfaces. GAFA 19-4, 943–988 (2009)
Dahmani F., Fujiwara K.: Copies of one-ended groups in mapping class groups. Groups Geom. Dyn. 3(3), 359–377 (2009)
Gromov, M.: Hyperbolic groups. In: Essays in Group Theory, Math. Sci. Res. Inst. Publ., vol. 8, pp. 75–263. Springer, New York (1987)
Minsky Y.: The classification of Kleinian surface groups. I. Models and bounds. Ann. Math. (2) 171(1), 1–107 (2010)
Sela Z.: Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups. II. Geom. Funct. Anal. 7(3), 561–593 (1997)
White, M.: Some Bounds for Closed Hyperbolic 3-Manifolds. Ph.D. Thesis, Univ. of California, Santa Barbara (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barnard, J. Bounding surface actions on hyperbolic spaces. Geom Dedicata 164, 311–318 (2013). https://doi.org/10.1007/s10711-012-9775-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-012-9775-4