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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.15820 |
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| _version_ | 1866912284003008512 |
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| author | Goldman, Katherine Herron, Amy |
| author_facet | Goldman, Katherine Herron, Amy |
| contents | We show that the piecewise Euclidean Moussong metric on the Deligne complex of the Artin group of type $B_3$ is $\mathrm{CAT}(0)$. We do this by establishing a criteria for a complex made of $B_3$ simplices to be $\mathrm{CAT}(1)$ in terms of embedded edge paths, which in particular applies to the spherical Deligne complex of type $B_3$. This provides one more step to showing that the Moussong metric is $\mathrm{CAT}(0)$ for any 3-dimensional Artin group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Deligne Complex for the $B_3$ Artin Group Goldman, Katherine Herron, Amy Group Theory Metric Geometry 20F65 (Primary) 20F36, 57M60 (Secondary) We show that the piecewise Euclidean Moussong metric on the Deligne complex of the Artin group of type $B_3$ is $\mathrm{CAT}(0)$. We do this by establishing a criteria for a complex made of $B_3$ simplices to be $\mathrm{CAT}(1)$ in terms of embedded edge paths, which in particular applies to the spherical Deligne complex of type $B_3$. This provides one more step to showing that the Moussong metric is $\mathrm{CAT}(0)$ for any 3-dimensional Artin group. |
| title | The Deligne Complex for the $B_3$ Artin Group |
| topic | Group Theory Metric Geometry 20F65 (Primary) 20F36, 57M60 (Secondary) |
| url | https://arxiv.org/abs/2503.15820 |