Limit sets of relatively hyperbolic groups

被引：0
作者：
Wen-yuan Yang
机构：
[1] Hunan University,College of Mathematics and Econometrics
[2] Universite de Lille 1,U.F.R. de Mathematiques
来源：
Geometriae Dedicata | 2012年 / 156卷
关键词：
Dynamical quasiconvexity; Relatively hyperbolic group; Limit set; Floyd boundary; 20F65; 20F67;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known results on limit sets of geometrically finite Kleinian groups are derived in general convergence groups. We also establish dynamical quasiconvexity of undistorted subgroups in finitely generated groups with nontrivial Floyd boundaries.
引用
收藏
页码：1 / 12
页数：11
相关论文
共 29 条
  • [1] Anderson J.(1991)On the finitely generated intersection property for Kleinian groups Complex Var. Theor. Appl. 17 111-112
  • [2] Anderson J.(1995)Intersections of topologically tame subgroups of Kleinian groups J. Anal. Math. 65 77-94
  • [3] Anderson J.(1996)The limit set intersection theorem for finitely generated Kleinian groups Math. Res. Lett. 3 675-692
  • [4] Drutu C.(2005)Tree-graded spaces and asymptotic cones of groups With an appendix by D. Osin and M. Sapir. Topology 44 959-1058
  • [5] Sapir M.(2003)Combination of convergence groups Geom. Topol. 7 933-963
  • [6] Dahmani F.(1998)Relatively hyperbolic groups Geom. Funct. Anal. 8 810-840
  • [7] Farb B.(1980)Group completions and limit sets of Kleinian groups Invent. Math. 57 205-218
  • [8] Floyd W.(2009)Expansive convergence groups are relatively hyperbolic Geom. Funct. Anal. 19 137-169
  • [9] Gerasimov V.(1998)Widths of subgroups Trans. Am. Math. Soc. 350 321-329
  • [10] Gitik R.(2010)Relative hyperbolicity and relative quasiconvexity for countable groups Algebr. Geom. Topol. 10 1807-1856
123