Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions

Pages: 69 – 78

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n1.a5

Authors

Kouyemon Iriye (Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Japan)

Daisuke Kishimoto (Department of Mathematics, Kyoto University, Kyoto, Japan)

Abstract

Let $K$ be a simplicial complex such that the Taylor resolution for its Stanley–Reisner ring is minimal. We prove that the following conditions are equivalent: (1) $K$ is Golod; (2) any two minimal non-faces of $K$ are not disjoint; (3) the moment-angle complex for $K$ is homotopy equivalent to a wedge of spheres; (4) the decomposition of the suspension of the polyhedral product $\mathcal{Z}_K (C \underline{X}, \underline{X})$ due to Bahri, Bendersky, Cohen and Gitler desuspends.

Keywords

Stanley–Reisner ring, Golod property, Taylor resolution, polyhedral product, fat wedge filtration

2010 Mathematics Subject Classification

13F55, 55P15

Received 9 May 2017

Received revised 22 August 2017

Published 27 December 2017