Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Two-dimensional Golod complexes

Pages: 215 – 226

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a12


Kouyemon Iriye (Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Japan)

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


We characterize two-dimensional Golod complexes combinatorially by vertex-breakability and topologically by the fatwedge filtration of a polyhedral product. Applying the characterization, we consider a difference between Golodness over fields and rings, which enables us to give a two-dimensional simple Golod complex over any field such that the corresponding moment-angle complex is not a suspension.


Stanley–Reisner ring, Golod property, neighborly complex, polyhedral product, fat-wedge filtration

2010 Mathematics Subject Classification

13F55, 55P15

Received 8 November 2020

Accepted 29 November 2020

Published 7 July 2021