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.