ON BOUNDARIES OF COXETER GROUPS AND TOPOLOGICAL FRACTAL STRUCTURES

被引：3

作者：

Hosaka, Tetsuya ^{[1
]}

机构：

[1] Utsunomiya Univ, Fac Educ, Dept Math, Utsunomiya, Tochigi 3218505, Japan

来源：

TSUKUBA JOURNAL OF MATHEMATICS | 2011年 / 35卷 / 02期

关键词：

Coxeter group; boundary; CAT(0) space; Davis complex; rank-one isometry; minimal; fractal;

D O I：

10.21099/tkbjm/1331658700

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, based on research on rank-one isometries by W. Ballmann and M. Brin and recent research on rank-one isometries of Coxeter groups by P. Caprace and K. Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter group and introduce some observations on boundaries of CAT(0) groups with rank-one isometries.

引用

页码：153 / 160

页数：8

共 50 条

[21] Coxeter groups and Kahler groups
Py, Pierre
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2013, 155 (03) : 557 - 566
[22] Arboreal structures on groups and the associated boundaries
Anna Erschler
Vadim A. Kaimanovich
[J]. Geometric and Functional Analysis, 2023, 33 : 694 - 748
[23] Arboreal structures on groups and the associated boundaries
Erschler, Anna
Kaimanovich, Vadim A.
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2023, 33 (03) : 694 - 748
[24] Coxeter groups, Coxeter monoids and the Bruhat order
Toby Kenney
[J]. Journal of Algebraic Combinatorics, 2014, 39 : 719 - 731
[25] Coxeter groups, Coxeter monoids and the Bruhat order
Kenney, Toby
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2014, 39 (03) : 719 - 731
[26] Topological structures ofθ-subsets in symplectic groups
Yiming Long
[J]. Acta Mathematica Sinica, 1999, 15 : 255 - 268
[27] Right-angled Coxeter groups with the n-dimensional Sierpiski compacta as boundaries
Swiatkowski, Jacek
[J]. JOURNAL OF TOPOLOGY, 2017, 10 (04) : 970 - 994
[28] Hyperbolic right-angled Coxeter groups with boundaries as a Sierpinski carpet and a Menger curve
Chinen, Naotsugu
Hosaka, Tetsuya
[J]. TOPOLOGY AND ITS APPLICATIONS, 2019, 260 : 70 - 85
[29] Topological Structures of ω-subsets in Symplectic Groups
Yiming Long
[J]. Acta Mathematica Sinica,English Series, 1999, 15 (02) : 255 - 268
[30] Duality theorems and topological structures of groups
Tatsuuma, Nobuhiko
[J]. KYOTO JOURNAL OF MATHEMATICS, 2014, 54 (01) : 75 - 101

← 1 2 3 4 5 →