Cactus groups from the viewpoint of geometric group theory

Anthony Genevois

Cactus groups from the viewpoint of geometric group theory

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arxiv 2212.03494 v1 pith:LZFXCBAQ submitted 2022-12-07 math.GR math.AT

Anthony Genevois This is my paper · ORCID

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keywords groupscactusgeometricgrouptheoryacylindricallyappeararticle

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Cactus groups and their pure subgroups appear in various fields of mathematics and are currently attracting attention from diverse mathematical communities. They share similarities with both right-angled Coxeter groups and braid groups. In this article, our goal is to highlight the tools offered by geometric group theory for the study of these groups. Among the new contributions made possible thanks to this geometric perspective, we describe an explicit and efficient solution to the conjugacy problem, and we prove that cactus groups are virtually cocompact special and acylindrically hyperbolic.

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Trickle groups
math.GR 2024-12 conditional novelty 6.0 of 10

Trickle groups unify right-angled Artin/Coxeter groups, cactus groups, Thompson group F, and ordered quandle groups, and they all inherit a terminating and confluent rewriting system and a solution to the word problem.

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