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

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