Quasi-flats in semihyperbolic groups
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- by P. Papasoglu PDF
- Proc. Amer. Math. Soc. 126 (1998), 1267-1273 Request permission
Abstract:
We prove that the Cayley graph of a group which is semihyperbolic but not hyperbolic contains a subset quasi-isometric to $\mathbb {R}^{2}$.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
- Martin R. Bridson, On the existence of flat planes in spaces of nonpositive curvature, Proc. Amer. Math. Soc. 123 (1995), no. 1, 223–235. MR 1273477, DOI 10.1090/S0002-9939-1995-1273477-8
- Patrick Eberlein, Geodesic flow in certain manifolds without conjugate points, Trans. Amer. Math. Soc. 167 (1972), 151–170. MR 295387, DOI 10.1090/S0002-9947-1972-0295387-4
- David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Michael S. Paterson, and William P. Thurston, Word processing in groups, Jones and Bartlett Publishers, Boston, MA, 1992. MR 1161694
- 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}
- 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
- Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89, Springer-Verlag, Berlin-New York, 1977. MR 0577064
- L.Mosher, U.Oertel, Spaces which are not negatively curved,, preprint, Rutgers University.
- P. Papasoglu, Strongly geodesically automatic groups are hyperbolic, Invent. Math. 121 (1995), no. 2, 323–334. MR 1346209, DOI 10.1007/BF01884301
- H.Short, Groups and combings, preprint ENS Lyon.
- V. Schroeder, On the fundamental group of a visibility manifold, Math. Z. 192 (1986), no. 3, 347–351. MR 845208, DOI 10.1007/BF01164010
Additional Information
- P. Papasoglu
- Affiliation: Department of Mathematics, University of Paris-Sud, Bat 425, Orsay, France
- Email: panos@matups.matups.fr
- Received by editor(s): November 28, 1995
- Received by editor(s) in revised form: October 15, 1996
- Communicated by: James West
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1267-1273
- MSC (1991): Primary 20F32
- DOI: https://doi.org/10.1090/S0002-9939-98-04467-0
- MathSciNet review: 1459144