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arXiv · 2503.15820

The Deligne Complex for the $B_3$ Artin Group

Katherine Goldman·Amy Herron
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Abstract

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.

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Katherine Goldman, Amy Herron. 2025-03-20. The Deligne Complex for the $B_3$ Artin Group. https://arxiv.org/abs/2503.15820

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