Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

On polyhedral product spaces over polyhedral joins

Pages: 259 – 280

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a13


Elizabeth Vidaurre (Department of Mathematics, University of Rochester, New York, U.S.A.)


The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler’s $J$-construction and simplicial wedge construction. This article gives a cohomological decomposition of a polyhedral product over a polyhedral join. A formula for the Hilbert–Poincaré series is given, which generalizes Ayzenberg’s formula for the moment-angle complex.


cohomology ring, moment-angle complex, simplicial complex, Stanley–Reisner ring, simplicial wedge construction

2010 Mathematics Subject Classification

05E45, 13F55, 14F45

Received 29 September 2017

Received revised 7 March 2018

Published 13 June 2018