Simplicial pseudohyperplane arrangements give weak Garside groups

Katherine Goldman

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arXiv · 2310.06919

Simplicial pseudohyperplane arrangements give weak Garside groups

Katherine Goldman

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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.

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Katherine Goldman. 2023-10-10. Simplicial pseudohyperplane arrangements give weak Garside groups. https://arxiv.org/abs/2310.06919

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