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Growth of relatively hyperbolic groups
Author(s):
Xiangdong
Xie
Journal:
Proc. Amer. Math. Soc.
135
(2007),
695-704.
MSC (2000):
Primary 20F65
Posted:
September 15, 2006
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Abstract:
We show that a finitely generated group that is hyperbolic relative to a collection of proper subgroups either is virtually cyclic or has uniform exponential growth.
References:
-
- [AN]
- R. Alperin, G. Noskov, Nonvanishing of algebraic entropy for geometrically finite groups of isometries of Hadamard manifolds, preprint(2004).
- [B]
- B. Bowditch, Relatively hyperbolic groups, preprint(1999).
- [D]
- C. Drutu, Quasi-isometric rigidity of groups, preprint(2004).
- [EMO]
- A. Eskin, S. Mozes, H. Oh, Uniform exponential growth for linear groups, Int. Math. Res. Not. 2002, no. 31, 1675-1683. MR 1916428 (2003g:20074)
- [F]
- B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no. 5, 810-840. MR 1650094 (99j:20043)
- [G]
- M. Gromov, Hyperbolic Groups, in `` Essays in Group Theory" (ed. S. Gersten) M.S.R.I. Publications No.8, Springer-Verlag(1987) 75-263. MR 0919829 (89e:20070)
- [GD]
- R. Grigorchuk, P. de la Harpe, One-relator groups of exponential growth have uniformly exponential growth, translation in Math. Notes 69 (2001), no. 3-4, 575-577. MR 1846003 (2002b:20041)
- [GhD]
- E. Ghys and P. de la Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics 83.
- [HK]
- G. Hruska, B. Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005), 1501-1538. MR 2175151
- [K]
- M. Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998), no. 5, 1441-1453. MR 1662255 (99m:20080)
- [O1]
- D. Osin, Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 (2006), no. 843, vi+100pp. MR 2182268
- [O2]
- D. Osin, The entropy of solvable groups, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 907-918. MR 1992670 (2004f:20065)
- [O3]
- D. Osin, Weakly amenable groups, Contemp. Math., 298 (2002), 105-113.
- [W]
- J. Wilson, On exponential growth and uniformly exponential growth for groups, Invent. Math. 155 (2004), no. 2, 287-303. MR 2031429 (2004k:20085)
- [Y]
- A. Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004), 41-89. MR 2039323 (2005e:20064)
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Additional Information:
Xiangdong
Xie
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221
Address at time of publication:
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email:
xxie@math.uc.edu
DOI:
10.1090/S0002-9939-06-08537-6
PII:
S 0002-9939(06)08537-6
Keywords:
Exponential growth,
uniform exponential growth,
relatively hyperbolic groups,
geometrically finite groups.
Received by editor(s):
April 10, 2005
Received by editor(s) in revised form:
October 18, 2005
Posted:
September 15, 2006
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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