论文标题
右角ARTIN组，多面体产品和TC生成功能
Right-angled Artin groups, polyhedral products and the TC-generating function
论文作者
论文摘要
对于图$γ$，令$ k（H_γ，1）$表示与右角ARTIN（RAA）组相关的Eilenberg-Mac Lane空间$H_γ$由$γ$定义。我们使用$γ$的组合学与$ k（H_γ，1）$的拓扑复杂性之间的关系来解释，并推广到更高的TC领域，Dranishnikov的观察到，覆盖空间的拓扑复杂性可能大于基本空间的拓扑复杂性。在此过程中，对于任何正整数$ n $，我们构建一个图$ \ Mathcal {o} _n $，其TC生成功能具有$ n $的多项式分子。此外，我们以$ K（H_γ，1）$可以实现为多面体产品的事实，我们研究了更通用的多面体产品空间的LS类别和拓扑复杂性。特别是，我们使用强轴向图的概念，以给出估计值，在许多情况下，是多面体产品的拓扑复杂性，其因子是真实的投射空间。我们的估计在RAA组的情况下表现出不存在的混合CAT-TC现象。
For a graph $Γ$, let $K(H_Γ,1)$ denote the Eilenberg-Mac Lane space associated to the right-angled Artin (RAA) group $H_Γ$ defined by $Γ$. We use the relationship between the combinatorics of $Γ$ and the topological complexity of $K(H_Γ,1)$ to explain, and generalize to the higher TC realm, Dranishnikov's observation that the topological complexity of a covering space can be larger than that of the base space. In the process, for any positive integer $n$, we construct a graph $\mathcal{O}_n$ whose TC-generating function has polynomial numerator of degree $n$. Additionally, motivated by the fact that $K(H_Γ,1)$ can be realized as a polyhedral product, we study the LS category and topological complexity of more general polyhedral product spaces. In particular, we use the concept of a strong axial map in order to give an estimate, sharp in a number of cases, of the topological complexity of a polyhedral product whose factors are real projective spaces. Our estimate exhibits a mixed cat-TC phenomenon not present in the case of RAA groups.
