Fat-wedge filtration and decomposition of polyhedral products

DOI10.1215/21562261-2017-0038zbMATH Open1455.55007arXiv1412.4866OpenAlexW3098519040WikidataQ129462985 ScholiaQ129462985MaRDI QIDQ2312757

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Publication date: 17 July 2019

Published in: (Search for Journal in Brave)

Abstract: The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex $K$ is studied by investigating its filtration called the fat wedge filtration. We give a sufficient condition for decomposing the polyhedral product in terms of the fat wedge filtration of the real moment-angle complex for $K$, which is a desuspension of the decomposition of the suspension of the polyhedral product due to Bahri, Bendersky, Cohen, and Gitler. We show that the condition also implies a strong connection with the Golodness of $K$, and is satisfied when $K$ is dual sequentially Cohen-Macaulay over $mathbbZ$ or $lceilfracdimK2ceil$-neighborly so that the polyhedral product decomposes. Specializing to moment-angle complexes, we also give a necessary and sufficient condition for their decomposition and co-H-structures in terms of their fat wedge filtration.

Full work available at URL: https://arxiv.org/abs/1412.4866

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