Moment-angle complexes from simplicial posets

We extend the construction of moment-angle complexes to simplicial posets by associating a certain T ^m -space Z _S to an arbitrary simplicial poset S on m vertices. Face rings ℤS] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤS] by topological methods. The space Z _S has many important topological properties of the original moment-angle complex Z _K associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of Z _S is isomorphic to the Tor-algebra of the face ring ℤS]. This leads directly to a generalisation of Hochster’s theorem, expressing the algebraic Betti numbers of the ring ℤS] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of Z _S from below by proving the toral rank conjecture for the moment-angle complexes Z _S .