Simplicial pseudohyperplane arrangements give weak Garside groups

Goldman, Katherine

doi:10.1090/proc/17059

Simplicial pseudohyperplane arrangements give weak Garside groups
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by Katherine M. Goldman;

Proc. Amer. Math. Soc. 153 (2025), 2283-2297

DOI: https://doi.org/10.1090/proc/17059

Published electronically: March 24, 2025

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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 the 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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Simplicial pseudohyperplane arrangements give weak Garside groups
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Abstract: