A METRIZABLE TOPOLOGY ON THE CONTRACTING BOUNDARY OF A GROUP

被引：20
作者：
Cashen, Christopher H. [1 ]
Mackay, John M.
机构：
[1] Univ Vienna, Fac Math, Oskar Morgenstern pl 1, A-1090 Vienna, Austria
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 03期
基金：
奥地利科学基金会; 美国国家科学基金会; 英国工程与自然科学研究理事会;
关键词：
Contracting boundary; Morse boundary; boundary at infinity; contracting geodesic; divagation; QUASI-GEODESICS; STABILITY; GEOMETRY; PROJECTIONS; DIVERGENCE; SPACES;
D O I：
10.1090/tran/7544
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrically relevant, quasi-isometry invariant topology on the contracting boundary. When the space is the Cayley graph of a finitely generated group we show that our new topology is metrizable.
引用
收藏
页码：1555 / 1600
页数：46
相关论文
共 41 条
[1]  
Abbott C, 2017, ARXIV170506219
[2]   Strongly contracting geodesics in Outer Space [J].
Algom-Kfir, Yael .
GEOMETRY & TOPOLOGY, 2011, 15 (04) :2181-2233
[3]   Pulling back stability with applications to Out(Fn) and relatively hyperbolic groups [J].
Aougab, Tarik ;
Durham, Matthew Gentry ;
Taylor, Samuel J. .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2017, 96 :565-583
[4]  
Arzhantseva GN, 2017, DOC MATH, V22, P1193
[5]  
Arzhantseva Goulnara N., 2016, ARXIV160203767V2
[6]  
Behrstock Jason, 2017, ARXIV170503984V2
[7]   Asymptotic geometry of the mapping class group and Teichmuller space [J].
Behrstock, Jason A. .
GEOMETRY & TOPOLOGY, 2006, 10 :1523-1578
[8]   CONSTRUCTING GROUP ACTIONS ON QUASI-TREES AND APPLICATIONS TO MAPPING CLASS GROUPS [J].
Bestvina, Mladen ;
Bromberg, Ken ;
Fujiwara, Koji .
PUBLICATIONS MATHEMATIQUES DE L IHES, 2015, (122) :1-64
[9]   A CHARACTERIZATION OF HIGHER RANK SYMMETRIC SPACES VIA BOUNDED COHOMOLOGY [J].
Bestvina, Mladen ;
Fujiwara, Koji .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2009, 19 (01) :11-40
[10]   RELATIVELY HYPERBOLIC GROUPS [J].
Bowditch, B. H. .
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2012, 22 (03)
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