Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions

Pages: 69 – 78

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

Full Text (PDF format)

K.I. is supported by JSPS KAKENHI (No. 26400094), and D.K. is supported by JSPS KAKENHI (No. 25400087).

Received 9 May 2017

Received revised 22 August 2017

Published 27 December 2017