单形的λ的Buchstaber不变量
Buchstaber invariants of skeleta of a simplex
摘要：
矩-角复形$\mathcal{Z}_K$是与有限单纯复形$K$相关联的紧致拓扑空间。它被实现为多圆盘$(D^2)^m$的子空间，其中$m$是$K$中的顶点数，$D^2$是复数$\C$的单位圆盘，并且环面$(S^1)^m$对$(D^2)^m$的自然作用使$\mathcal{Z}_K$不变。$K$的Buchstaber不变量$s(K)$是存在秩为$s(K)$的子环面自由作用于$\mathcal{Z}_K$的最大整数。上面的故事是关于实数$\R$代替$\C$的，并且可以为$K$和$s(K)\leqq s_\R(K)$定义Buchstaber不变量的实数类似物，表示为$s_\R(K)$。当$K$是单纯形的骨架时，本文将对$s_\R(K)$进行一些计算.我们采取两种方法来寻找$s_\R(K)$，后者原来是一个整数线性规划问题，并有独立的利益。
英文摘要：
A moment-angle complex $\mathcal{Z}_K$ is a compact topological space associated with a finite simplicial complex $K$. It is realized as a subspace of a polydisk $(D^2)^m$, where $m$ is the number of vertices in $K$ and $D^2$ is the unit disk of the complex numbers $\C$, and the natural action of a torus $(S^1)^m$ on $(D^2)^m$ leaves $\mathcal{Z}_K$ invariant. The Buchstaber invariant $s(K)$ of $K$ is the maximum integer for which there is a subtorus of rank $s(K)$ acting on $\mathcal{Z}_K$ freely. The story above goes over the real numbers $\R$ in place of $\C$ and a real analogue of the Buchstaber invariant, denoted $s_\R(K)$, can be defined for $K$ and $s(K)\leqq s_\R(K)$. In this paper we will make some computations of $s_\R(K)$ when $K$ is a skeleton of a simplex. We take two approaches to find $s_\R(K)$ and the latter one turns out to be a problem of integer linear programming and of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
