Combination of convergence groups

被引：148
作者：
Dahmani, F [1 ]
机构：
[1] ETH Zentrum, Forschungsinst Math, CH-8092 Zurich, Switzerland
来源：
GEOMETRY & TOPOLOGY | 2003年 / 7卷
关键词：
relatively hyperbolic groups; geometrically finite convergence groups; combination theorem; limit groups;
D O I：
10.2140/gt.2003.7.933
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to contruct a boundary for a group that is an acylindrical amalgamation of relatively hyperbolic groups over a fully quasi- convex subgroup. We apply our result to Sela's theory on limit groups and prove their relative hyperbolicity. We also get a proof of the Howson property for limit groups.
引用
收藏
页码：933 / 963
页数：31
相关论文
共 32 条
[1]   LIMIT POINTS OF KLEINIAN GROUPS AND FINITE SIDED FUNDAMENTAL POLYHEDRA [J].
BEARDON, AF ;
MASKIT, B .
ACTA MATHEMATICA, 1974, 132 (1-2) :1-12
[2]  
Bestvina M, 1996, MICH MATH J, V43, P123
[3]  
Bestvina M, 1996, J DIFFER GEOM, V43, P783
[4]  
BESTVINA M, 1992, J DIFFER GEOM, V35, P85
[5]   A topological characterisation of hyperbolic groups [J].
Bowditch, BH .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 11 (03) :643-667
[6]   GEOMETRICAL FINITENESS WITH VARIABLE NEGATIVE CURVATURE [J].
BOWDITCH, BH .
DUKE MATHEMATICAL JOURNAL, 1995, 77 (01) :229-274
[7]  
Bowditch BH, 1999, GEOMETRIC GROUP THEORY DOWN UNDER, P23
[8]  
BOWDITCH BH, 1999, RELATIVELY HYPERBOLI
[9]   Classifying spaces and boundaries for relatively hyperbolic groups [J].
Dahmani, F .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2003, 86 :666-684
[10]  
DAHMANI F, 2003, THESIS STRASBOURG
1234