On Hochster's formula for a class of quotient spaces of moment-angle complexes

Abstract

Any finite simplicial complex $\mathcal{K}$ and a partition of the vertex set of $\mathcal{K}$ determines a canonical quotient space of the moment-angle complex of ${\mathcal K}$. We prove that the cohomology groups of such a space can be computed via some Hochster's type formula, which generalizes the usual Hochster's formula for the cohomology groups of moment-angle complexes. In addition, we show that the stable decomposition of moment-angle complexes can also be extended to such spaces. This type of spaces include all the quasitoric manifolds that are pullback from the linear models. And we prove that the moment-angle complex associated to a finite simplicial poset is always homotopy equivalent to one of such spaces.