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Groups acting on quasiconvex spaces and translation numbers
Author(s):
Aleksandar
Poleksic
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3177-3183.
MSC (2000):
Primary 20F65
Posted:
June 6, 2000
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Abstract:
We prove that groups acting geometrically on  -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:
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- 2.
- G. Conner, Translation numbers of groups acting on convex spaces, Brigham Young University, preprint (1994).
- 3.
- S.M. Gersten, H. Short, Rational subgroups of biautomatic groups, Annals of Math. 134 (1991), 125-158. MR 92g:20092
- 4.
- 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. CMP 92:02
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- M. Gromov, Hyperbolic groups, in Essays in Group Theory (S.M. Gersten, ed., Springer-Verlag, 1987), 75-263. MR 89e:20070
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- A. Poleksic, Translation numbers in negatively curved groups, Topol. and its Appl., to appear.
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- A. Poleksic, The boundary of a quasiconvex space, Topol. and its Appl., to appear.
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Additional Information:
Aleksandar
Poleksic
Affiliation:
Cold Spring Harbor Laboratory, P.O. Box 100, 1 Bungtown Road, Cold Spring Harbor, New York 11724
Email:
poleksic@cshl.org
DOI:
10.1090/S0002-9939-00-05537-4
PII:
S 0002-9939(00)05537-4
Received by editor(s):
January 5, 1999
Posted:
June 6, 2000
Additional Notes:
This paper forms a part of the author's Ph.D. dissertation written under the direction of P. Bowers at Florida State University.
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2000,
American Mathematical Society
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