Lickorish and Wallace proved that every closed oriented

three-manifold can be expressed as surgery on a link in the

three-sphere. This naturally leads to the question of which

three-manifolds are surgery on a knot. We give an obstruction coming from Heegaard Floer homology, and use it to construct infinitely many small Seifert fibered integer homology spheres which are not surgery on a knot. This is joint work with Cagri Karakurt and Tye Lidman.