Open manifolds, Ozsvath-Szabo invariants and Exotic R^4's
  We construct an invariant of open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R^4 for which the invariant is non-trivial, showing that X is an exotic R^4. 
Siddhartha Gadgil