Seifert fibered homology spheres with trivial Heegaard Floer homology

Abstract

We show that among Seifert fibered integer homology spheres, Poincare sphere (with either orientation) is the only non-trivial example which has trivial Heegaard Floer homology. Together with an earlier result, this shows that if an integer homology sphere has trivial Heegaard Floer homology, then it is a connected sum of a number of Poincare spheres and hyperbolic homology spheres.