Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-07T01:19:13.107Z Has data issue: false hasContentIssue false

Invariance of coarse median spaces under relative hyperbolicity

Published online by Cambridge University Press:  06 September 2012

BRIAN H. BOWDITCH*
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL. e-mail B.H.Bowditch@warwick.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that, for finitely generated groups, the property of admitting a coarse median structure is preserved under relative hyperbolicity.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2012

References

REFERENCES

[BaH]Bandelt, H.-J. and Hedlikova, J.Median algebras. Discrete Math. 45 (1983), 130.CrossRefGoogle Scholar
[BeM]Behrstock, J. A. and Minsky, Y. N. Centroids and the rapid decay property in mapping class groups. Preprint (2008).Google Scholar
[Bo1]Bowditch, B. H. Relatively hyperbolic groups. To appear in Internat. J. Algebra Comput.Google Scholar
[Bo2]Bowditch, B. H. Coarse median spaces and groups. To appear in Pacific J. Math.Google Scholar
[Bo3]Bowditch, B. H. Embedding median algebras in products of trees. Preprint, Warwick (2011).Google Scholar
[BrH]Bridson, M. and Haefliger, A.Metric spaces of non-positive curvature. Grundlehren der Math. Wiss. No. 319 (Springer 1999).Google Scholar
[F]Farb, B.Relatively hyperbolic groups. Geom. Funct. Anal. 8 (1998), 810840.CrossRefGoogle Scholar
[GhH]Ghys, E. and de la Harpe, P. (eds.). Sur les groupes hyperboliques d'après Mikhael Gromov. Prog. Math. 83 (Birkhäuser 1990).Google Scholar
[Gr]Gromov, M.Hyperbolic groups. In Essays in Group Theory. Math. Sci. Res. Inst. Publ. No. 8 (Springer 1987), 75263.CrossRefGoogle Scholar
[O]Osin, D. V.Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems. Mem. Amer. Math. Soc. 179 (2006).Google Scholar
[R]Roller, M. A.Poc-sets, median algebras and group actions, an extended study of Dunwoody's construction and Sageev's theorem. Habilitationschrift (Regensberg, 1998).Google Scholar