Fat wedge filtrations and decomposition of polyhedral products

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 $\mathbb{Z}$ or $\lceil \frac{\dim K}{2}\rceil$-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.

The paper includes the result of arXiv:1306.6221. To appear in Kyoto J. Math

References in corpus (2)

• The Golod property for Stanley-Reisner rings in varying characteristic
• Decompositions of suspensions of spaces involving polyhedral products

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