Fat-wedge filtration and decomposition of polyhedral products

摘要

The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complexK 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 showthat the condition also implies a strong connection with the Golodness of K, and it is satisfied when K is dual sequentially Cohen-Macaulay over Z or [ dimK/2]-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.