Abstract
The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex 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 , 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 , and it is satisfied when is dual sequentially Cohen–Macaulay over or -neighborly so that the polyhedral product decomposes. Specializing to the moment-angle complex, we prove that the similar condition on its fat-wedge filtrations is necessary and sufficient for its decomposition.
Citation
Kouyemon Iriye. Daisuke Kishimoto. "Fat-wedge filtration and decomposition of polyhedral products." Kyoto J. Math. 59 (1) 1 - 51, April 2019. https://doi.org/10.1215/21562261-2017-0038
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