Height in splittings of relatively hyperbolic groups

被引：1
|
作者：
Pal, Abhijit [1 ]
机构：
[1] IIT Kanpur, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India
来源：
GEOMETRIAE DEDICATA | 2021年 / 213卷 / 01期
关键词：
Relatively hyperbolic groups; Hyperbolic groups; Graph of Groups; COMBINATION THEOREM;
D O I：
10.1007/s10711-020-00571-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex in vertex groups, we prove that vertex groups are relatively quasiconvex if and only if all the vertex groups have finite relative height in the fundamental group.
引用
收藏
页码：121 / 135
页数：15
相关论文
共 50 条
  • [21] Growth of relatively hyperbolic groups
    Xie, Xiangdong
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (03) : 695 - 704
  • [22] Examples of Relatively Hyperbolic Groups
    Andrzej Szczepański
    Geometriae Dedicata, 2002, 93 : 139 - 142
  • [23] Endomorphisms of relatively hyperbolic groups
    Belegradek, Igor
    Szczepanski, Andrzej
    Belegradek, Oleg V.
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2008, 18 (01) : 97 - 110
  • [24] Examples of relatively hyperbolic groups
    Szczepanski, A
    GEOMETRIAE DEDICATA, 2002, 93 (01) : 139 - 142
  • [25] Quasiconvexity in relatively hyperbolic groups
    Gerasimov, Victor
    Potyagailo, Leonid
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2016, 710 : 95 - 135
  • [26] McCool groups of toral relatively hyperbolic groups
    Guirardel, Vincent
    Levitt, Gilbert
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2015, 15 (06): : 3485 - 3534
  • [27] Notes on Relatively Hyperbolic Groups and Relatively Quasiconvex Subgroups
    Matsuda, Yoshifumi
    Oguni, Shin-ichi
    Yamagata, Saeko
    TOKYO JOURNAL OF MATHEMATICS, 2015, 38 (01) : 99 - 123
  • [28] The generalised word problem in hyperbolic and relatively hyperbolic groups
    Ciobanu, Laura
    Holt, Derek
    Rees, Sarah
    JOURNAL OF ALGEBRA, 2018, 516 : 149 - 171
  • [29] QUASI-HYPERBOLIC PLANES IN RELATIVELY HYPERBOLIC GROUPS
    Mackay, John M.
    Sisto, Alessandro
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2020, 45 : 139 - 174
  • [30] Peripheral fillings of relatively hyperbolic groups
    Denis V. Osin
    Inventiones mathematicae, 2007, 167 : 295 - 326
12345