Irreducible homology S^1xS^2s which aren't zero surgery on knot

Abstract: I'll discuss constructions of manifolds with the homology of

S^1xS^2 which don't arise as Dehn surgery on a knot in S^3.  Our examples have weight one fundamental group and were constructed to answer a question of Aschenbrenner, Friedl and Wilton.  Moreover, they are not even homology cobordant to surgery on a knot in S^3.  One of our obstructions comes from d-invariants and was noted by Ozsvath and Szabo early on in the development of Heegaard Floer theory.     This is joint work with Tom Mark, Kyungbae Park, and Min Hoon Kim.