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

TL;DR

This paper extends Hochster's formula to compute the cohomology of a class of quotient spaces derived from moment-angle complexes, including quasitoric manifolds, and explores their stable decompositions.

Contribution

It generalizes Hochster's formula for these quotient spaces and shows their stable decomposition extends from moment-angle complexes.

Findings

Cohomology of quotient spaces computed via a generalized Hochster's formula.

Stable decomposition of moment-angle complexes extends to these quotient spaces.

Moment-angle complexes of finite simplicial posets are homotopy equivalent to these spaces.

Abstract

Any finite simplicial complex K and a partition of the vertex set of K determines a canonical quotient space of the moment-angle complex of 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.