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：

英国工程与自然科学研究理事会; 美国国家科学基金会; 奥地利科学基金会;

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

页码：1555 / 1600

页数：46

共 41 条

[11]

Bridson M. R., 1999, FUNDAMENTAL PRINCIPL, V319

[12] Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology [J].

Cashen, Christopher H. .

ANALYSIS AND GEOMETRY IN METRIC SPACES, 2016, 4 (01) :278-281

[13] Contracting boundaries of CAT(0) spaces [J].

Charney, Ruth ;

Sultan, Harold .

JOURNAL OF TOPOLOGY, 2015, 8 (01) :93-117

[14]

Charney Ruth, 2017, ARXIV170707028V1

[15] Morse boundaries of proper geodesic metric spaces [J].

Cordes, Matthew .

GROUPS GEOMETRY AND DYNAMICS, 2017, 11 (04) :1281-1306

[16] Stability and the Morse boundary [J].

Cordes, Matthew ;

Hume, David .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2017, 95 :963-988

[17]

Cordes Matthew, 2017, ARXIV170407598V1

[18]

Cordes Matthew, 2016, ARXIV160708899V1

[19] Spaces with nonpositive curvature and their ideal boundaries [J].

Croke, CB ;

Kleiner, B .

TOPOLOGY, 2000, 39 (03) :549-556

[20] Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces [J].

Dahmani, F. ;

Guirardel, V. ;

Osin, D. .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 244 (1156) :1-+

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