### Buchstaber invariants of skeleta of a simplex

Yukiko Fukukawa and Mikiya Masuda
Source: Osaka J. Math. Volume 48, Number 2 (2011), 549-582.

#### Abstract

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 $\mathbb{C}$, 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 largest 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 $\mathbb{R}$ in place of $\mathbb{C}$ and a real analogue of the Buchstaber invariant, denoted $s_{\mathbb{R}}(K)$, can be defined for $K$ and $s(K)\leqq s_{\mathbb{R}}(K)$. In this paper we will make some computations of $s_{\mathbb{R}}(K)$ when $K$ is a skeleton of a simplex. We take two approaches to find $s_{\mathbb{R}}(K)$ and the latter one turns out to be a problem of integer linear programming and of independent interest.

First Page:
Primary Subjects: 57S17
Secondary Subjects: 90C10
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ojm/1315318353
Mathematical Reviews number (MathSciNet): MR2831986
Zentralblatt MATH identifier: 06005139

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