Moment-angle manifolds and connected sums of sphere products

Abstract

Corresponding to every finite simplicial complex $K$, there is a moment-angle complex $\mathcal{Z}_{K}$; if $K$ is a triangulation of a sphere, $\mathcal{Z}_{K}$ is a compact manifold. The question of whether $\mathcal{Z}_{K}$ is a connected sum of sphere products was considered in [3, Section 11]. So far, all known examples of moment-angle manifolds which are homeomorphic to connected sums of sphere products have the property that every product is of exactly two spheres. In this paper, we give a example whose cohomology ring is isomorphic to that of a connected sum of sphere products with one product of three spheres. We also give some general properties of this kind of moment-angle manifolds.