Triple Cup Products in Heegaard Floer Homology

Manolescu and Ozsvath have recently developed a formula for calculating the Heegaard Floer homologies of integral surgery on a link. We use their link surgery formula to give a complete calculation (mod 2) of the infinity flavor of Heegaard Floer homology for a torsion Spin c structure on any closed, orientable three-manifold in terms of the cup product structure on its integral cohomology ring.