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Autori principali: Goldman, Katherine, Herron, Amy
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2503.15820
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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