Heegaard Floer invariants for homology S^1 \times S^3s
Heegaard Floer invariants for homology S^1 \times S^3s

Adam Levine, Princeton University
Fine Hall 314
Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented 4manifold X with the homology of S^1 \times S^3. Specifically, we show that for any smoothly embedded 3manifold Y representing a generator of H_3(X), a suitable version of the Heegaard Floer d invariant of Y, defined using twisted coefficients, is a diffeomorphism invariant of X. We show how this invariant can be used to obstruct embeddings of certain types of 3manifolds, including those obtained as a connected sum of a rational homology 3sphere and any number of copies of S^1 \times S^2. We also give similar obstructions to embeddings in certain open 4manifolds, including exotic R^4s. This is joint work with Danny Ruberman.