On the non-discreteness of automorphism groups of Cayley graphs of Coxeter groups

Federico Berlai; Michal Ferov

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arXiv · 2302.04444

On the non-discreteness of automorphism groups of Cayley graphs of Coxeter groups

Federico Berlai·Michal Ferov

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Abstract

In this work we characterise Cayley graphs of Coxeter groups with respect to the standard generating set that admit uncountable vertex stabilisers. As a corollary, we fully identify finitely generated Coxeter groups for which the automorphism group of their Cayley graph with respect to the standard generating set is not discrete when equipped with the permutation topology. As an application, we also provide new explicit constructions of vertex-transitive graphs of infinite degree that have locally compact automorphism groups.

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Federico Berlai, Michal Ferov. 2023-02-09. On the non-discreteness of automorphism groups of Cayley graphs of Coxeter groups. https://arxiv.org/abs/2302.04444

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