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# Homology, Homotopy and Applications

## Volume 20 (2018)

### Number 1

### Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions

Pages: 69 – 78

#### Authors

#### 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

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