A counterexample to questions about boundaries, stability, and commensurability
Jason Behrstock
TL;DR
This paper constructs specific right-angled Coxeter groups that serve as counterexamples to several open questions regarding their boundaries, subgroup properties, and commensurability classifications.
Contribution
It introduces a family of Coxeter groups that challenge existing assumptions about boundaries, subgroup stability, and commensurability in geometric group theory.
Findings
Counterexamples to boundary stability questions
Counterexamples to one-endedness of stable subgroups
Counterexamples to commensurability classifications
Abstract
We construct a family of right-angled Coxeter groups which provide counter-examples to questions about the stable boundary of a group, one-endedness of quasi-geodesically stable subgroups, and the commensurability types of right-angled Coxeter groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology