A cup product pairing and time-duality for discrete dynamical systems

With each isolating block for a homeomorphism of an orientable manifold we associate a cup product pairing. Up to an isomorphism, this is a pairing of the discrete Conley indices of the homeomorphism and its inverse on the isolating block. We show that this pairing is nondegenerate. As a corollary we prove a time duality result for the discrete Conley index.