Simplicial pseudohyperplane arrangements give weak Garside groups
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909323650662400 |
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| author | Goldman, Katherine |
| author_facet | Goldman, Katherine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06919 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simplicial pseudohyperplane arrangements give weak Garside groups Goldman, Katherine Group Theory Algebraic Topology Combinatorics 20F65 (Primary), 05B35, 32S22 (Secondary) 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. |
| title | Simplicial pseudohyperplane arrangements give weak Garside groups |
| topic | Group Theory Algebraic Topology Combinatorics 20F65 (Primary), 05B35, 32S22 (Secondary) |
| url | https://arxiv.org/abs/2310.06919 |