Simplicial pseudohyperplane arrangements give weak Garside groups
Group Theory
2024-09-25 v2 Algebraic Topology
Combinatorics
Abstract
In this note we connect the language of Bessis's Garisde categories with Salvetti's metrical-hemisphere complexes in order to find new examples of weak Garside groups. As our main example, we show that the fundamental group of the (appropriately defined) complexified complement of a pseudohyperplane arrangement is a weak Garside group. As a consequence of the Folkman-Lawrence topological realization theorem, we also show that fundamental group of the Salvetti complex of a ("simplicial") oriented matroid is a weak Garside group. This provides novel examples of weak Garside groups.
Cite
@article{arxiv.2310.06919,
title = {Simplicial pseudohyperplane arrangements give weak Garside groups},
author = {Katherine Goldman},
journal= {arXiv preprint arXiv:2310.06919},
year = {2024}
}
Comments
Updated following referee report. To appear in Proc. Amer. Math Soc