Simplicial pseudohyperplane arrangements give weak Garside groups
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2023
- DOI:
- 10.48550/arXiv.2310.06919
- arXiv:
- arXiv:2310.06919
- Bibcode:
- 2023arXiv231006919G
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Algebraic Topology;
- Mathematics - Combinatorics;
- 20F65 (Primary);
- 05B35;
- 32S22 (Secondary)
- E-Print:
- Updated following referee report. To appear in Proc. Amer. Math Soc