Right-angled Coxeter groups with totally disconnected Morse boundaries

被引：0

作者：

Karrer, Annette ^{[1
,2
,3
]}

机构：

[1] Karlsruhe Inst Technol, Dept Math, Karlsruhe, Germany

[2] Technion Israel Inst Technol, Dept Math, Haifa, Israel

[3] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada

来源：

GEOMETRIAE DEDICATA | 2023年 / 217卷 / 04期

基金：

以色列科学基金会;

关键词：

RACGs; Morse boundary; CAT(0)space with block decomposition; Amalgamation; Contracting boundary; CAT(0); DIVERGENCE;

D O I：

10.1007/s10711-023-00798-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces a new class of right-angled Coxeter groups with totally disconnected Morse boundaries. We construct this class recursively by examining howthe Morse boundary of a right-angled Coxeter group changes if we glue a graph to its defining graph. More generally, we present a method to construct amalgamated free products of CAT(0) groups with totally disconnected Morse boundaries that act geometrically on CAT(0) spaces that have a treelike block decomposition. We deduce a new proof for the result of CharneyCordes-Sisto (Complete topological descriptions of certain Morse boundaries, Groups Geom. Dyn. 17(1),157-184 (2023)) that every right-angled Artin group has totally disconnected Morse boundary, and discuss concrete examples of surface amalgams studied by Ben-Zvi (Boundaries of groups with isolated flats are path connected. arXiv:1909.12360, 2019).

引用

页数：40

共 50 条

[1] Right-angled Coxeter groups with totally disconnected Morse boundaries
Annette Karrer
[J]. Geometriae Dedicata, 2023, 217
[2] Morse subgroups and boundaries of random right-angled Coxeter groups
Tim Susse
[J]. Geometriae Dedicata, 2023, 217
[3] Surprising circles in Morse boundaries of right-angled Coxeter groups
Graeber, Marius
Karrer, Annette
Lazarovich, Nir
Stark, Emily
[J]. TOPOLOGY AND ITS APPLICATIONS, 2021, 294
[4] Morse subgroups and boundaries of random right-angled Coxeter groups
Susse, Tim
[J]. GEOMETRIAE DEDICATA, 2023, 217 (02)
[5] Boundaries of right-angled Coxeter groups with manifold nerves
Fischer, H
[J]. TOPOLOGY, 2003, 42 (02) : 423 - 446
[6] Right-angled Artin groups are commensurable with right-angled Coxeter groups
Davis, MW
Januszkiewicz, T
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2000, 153 (03) : 229 - 235
[7] Right-angled Artin subgroups of right-angled Coxeter and Artin groups
Dani, Pallavi
Levcovitz, Ivan
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2024, 24 (02):
[8] A complex for right-angled coxeter groups
Droms, C
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (08) : 2305 - 2311
[9] DIVERGENCE IN RIGHT-ANGLED COXETER GROUPS
Dani, Pallavi
Thomas, Anne
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (05) : 3549 - 3577
[10] Cells and representations of right-angled Coxeter groups
Mikhail Belolipetsky
[J]. Selecta Mathematica, 2004, 10 (3)

← 1 2 3 4 5 →