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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Quasi-flats in semihyperbolic groups

Author(s): P. Papasoglu
Journal: Proc. Amer. Math. Soc. 126 (1998), 1267-1273.
MSC (1991): Primary 20F32
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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:

[A-B]
J.Alonso, M.Bridson, Semihyperbolic groups, Proc. London Math. Soc. (3) 70 (1995), 56-114. MR 95j:20033

[Br]
M.Bridson, On the existence of flat planes in spaces of non-positive curvature, Proc. Amer. Math. Soc. 123 (1995), 223-235. MR 95d:53048

[Eb]
P.Eberlein, Geodesic flow in certain manifolds without conjugate points, Trans. AMS,167, pp. 151-170, 1972. MR 45:4453

[Ep]
D.Epstein, Word Processing in Groups, Jones and Bartlett, Boston, 1992. MR 93i:20036

[Gr]
M.Gromov, Hyperbolic groups, in Essays in Group Theory, ed. by S.M.Gersten, MSRI publ., vol.8, Springer Verlag, 1987, pp. 75-263. MR 89e:20070

[G-S]
S.M.Gersten, H.Short, Rational subgroups of biautomatic groups, Annals of Math. 134, 1991, pp. 125-158. MR 92g:20092

[L-S]
R.Lyndon, P. Schupp, Combinatorial group theory, Springer Verlag, 1977. MR 58:28182

[M-O]
L.Mosher, U.Oertel, Spaces which are not negatively curved,, preprint, Rutgers University.

[P]
P.Papasoglu, Strongly geodesically automatic groups are hyperbolic, Inventiones Mathematicae, 121 (1995), 323-334. MR 96h:20073

[S]
H.Short, Groups and combings, preprint ENS Lyon.

[Sc]
V.Schroeder On the fundamental group of a visibility manifold, Math.Z. 192, pp. 347-351, 1986. MR 87i:53062


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Additional Information:

P. Papasoglu
Affiliation: Department of Mathematics, University of Paris-Sud, Bat 425, Orsay, France
Email: panos@matups.matups.fr

DOI: 10.1090/S0002-9939-98-04467-0
PII: S 0002-9939(98)04467-0
Received by editor(s): November 28, 1995
Received by editor(s) in revised form: October 15, 1996
Communicated by: James West
Copyright of article: Copyright 1998, American Mathematical Society


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