Open manifolds, Ozsváth–Szabó invariants and exotic R4’SR4’S

We construct an invariant of certain open four-manifolds using the Heegaard Floer theory of Ozsváth and Szabó. We show that there is a manifold X   homeomorphic to R4R4 for which the invariant is non-trivial, showing that X   is an exotic R4R4. This is the first invariant that detects exotic R4’sR4’s.