Growth of relatively hyperbolic groups

Proceedings of the American Mathematical Society

Volumn 135, Issue 3, 2007, Pages 695-704

  Xie, Xiangdong ^a,b  

^a UNIVERSITY OF CINCINNATI   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Exponential growth; Geometrically finite groups; Relatively hyperbolic groups; Uniform exponential growth

Indexed keywords

EID: 37549010230     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-06-08537-6     Document Type: Article

References (14)

1. R. Alperin, G. Noskov, Nonvanishing of algebraic entropy for geometrically finite groups of isometries of Hadamard manifolds, preprint(2004). B. Bowditch, Relatively hyperbolic groups, preprint(1999).
2. C. Drutu, Quasi-isometric rigidity of groups, preprint(2004).
3. A. Eskin, S. Mozes, H. Oh, Uniform exponential growth for linear groups, Int. Math. Res. Not. 2002, no.31, 1675-1683. MR1916428 (2003g:20074)
4. B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no.5, 810-840. MR1650094 (99j:20043)
5. M. Gromov, Hyperbolic Groups, in "Essays in Group Theory" (ed. S. Gersten) M.S.R.I. Publications No.8, Springer-Verlag(1987) 75-263. MR0919829 (89e:20070)
6. 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. MR1846003 (2002b:20041) (Pubitemid 33751595)
7. E. Ghys and P. de la Harpe, Sur les groupes hyperboliques d'apr̀es Mikhael Gromov, Progress in Mathematics 83.
8. G. Hruska, B. Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005), 1501-1538. MR2175151
9. M. Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998), no.5, 1441-1453. MR1662255 (99m:20080) (Pubitemid 128375132)
10. D. Osin, Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 (2006), no.843, vi+100pp. MR2182268
11. D. Osin, The entropy of solvable groups, Ergodic Theory Dynam. Systems 23 (2003), no.3, 907-918. MR1992670 (2004f:20065) (Pubitemid 36913933)
12. D. Osin, Weakly amenable groups, Contemp. Math., 298 (2002), 105-113.
13. J. Wilson, On exponential growth and uniformly exponential growth for groups, Invent. Math. 155 (2004), no.2, 287-303. MR2031429 (2004k:20085) (Pubitemid 38169959)
14. A. Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004), 41-89. MR2039323 (2005e:20064) (Pubitemid 38203223)