New Garside structures and applications to Artin groups

2023/05/19 by Haettel, Thomas, Huang, Jingyin · 1 citation
#05B35 #05C25 #06A12 #20E42 #20F36 #20F55 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2305.11622

Abstract

Garside groups are combinatorial generalizations of braid groups which enjoy many nice algebraic, geometric, and algorithmic properties. In this article we propose a method for turning the direct product of a group G by ℤ into a Garside group, under simple assumptions on G. This method gives many new examples of Garside groups, including groups satisfying certain small cancellation condition (including surface groups) and groups with a systolic presentation. Our method also works for a large class of Artin groups, leading to many new group theoretic, geometric and topological consequences for them. In particular, we prove new cases of K(π,1)-conjecture for some hyperbolic type Artin groups.

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• Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections

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