Stanley--Reisner rings of generalised truncation polytopes and their moment-angle manifolds

Abstract

We consider simple polytopes $P=v{c}^k({\Delta }^{n_1}\times \dots \times {\Delta }^{n_r})$, for $n_1\ge \dots \ge n_r\ge 1,r\ge 1,k\ge 0$, that is, $k$-vertex cuts of a product of simplices, and call them {\emph{generalized truncation polytopes}}. For these polytopes we describe the cohomology ring of the corresponding moment-angle manifold ${\mathcal{Z}}_P$ and explore some topological consequences of this calculation. We also examine minimal non-Golodness for their Stanley--Reisner rings and relate it to the property of ${\mathcal{Z}}_P$ being a connected sum of sphere products.

12 pages. arXiv admin note: text overlap with arXiv:1101.0066

Cited by in corpus (1)

• Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres