Simplicial pseudohyperplane arrangements give weak Garside groups
Abstract
In this note we connect the language of Bessis's Garisde categories with Salvetti's metricalhemisphere 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 FolkmanLawrence 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2023
 DOI:
 10.48550/arXiv.2310.06919
 arXiv:
 arXiv:2310.06919
 Bibcode:
 2023arXiv231006919G
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 20F65 (Primary);
 05B35;
 32S22 (Secondary)
 EPrint:
 Updated following referee report. To appear in Proc. Amer. Math Soc