Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres

We prove that the moment-angle complex ZK corresponding to a 3-dimensional simplicial sphere K has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) K is the boundary of a 4-dimensional cross-polytope, or (b) the one-skeleton of K is a chordal graph, or (c) there are only two missing edges in K and they form a chordless 4-cycle. For simplicial spheres K of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism H^* (ZK) H^* (M) where M is a connected sum of products of spheres.