Title: The Deligne Complex for the $B_3$ Artin Group Show Chinese title

Title: Deligne 用于$B_3$阿廷群的复形

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. Show Chinese abstract

Abstract: 我们证明了在Artin群类型$B_3$的Deligne复形上的分段欧几里得Moussong度量是$\mathrm{CAT}(0)$。 我们通过建立一个由$B_3$单形组成的复形在嵌入边路径意义上的$\mathrm{CAT}(1)$的标准，这尤其适用于类型$B_3$的球面Deligne复形。 这为证明Moussong度量对于任何三维Artin群都是$\mathrm{CAT}(0)$提供了又一步。