Profinite rigidity of affine Coxeter groups
Samuel M. Corson, Sam Hughes, Philip M\"oller, and Olga Varghese
TL;DR
This paper proves that affine Coxeter groups are uniquely determined by their profinite completions, establishing a form of algebraic rigidity for these groups.
Contribution
It introduces the first proof of profinite rigidity specifically for affine Coxeter groups, a significant class in geometric group theory.
Findings
Affine Coxeter groups are profinitely rigid.
Profinite completions uniquely determine affine Coxeter groups.
This result advances understanding of algebraic invariants in geometric group theory.
Abstract
We prove that affine Coxeter groups are profinitely rigid.
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Taxonomy
TopicsSupramolecular Self-Assembly in Materials · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics