Surgery Obstructions for Seifert Fibered Homology Spheres

Abstract

We examine surgeries on knots in S 3 to find surgery obstructions to Seifert fibered integral homology spheres. We find such obstructions by using Heegaard Floer and Knot Floer homology and the mapping cone formula for computing Heegaard Floer homology of surgery on a knot. Here however, we take a novel approach and use the toroidal structure, or the number of singular fibers of a homology sphere, to find obstructions. This approach allows us to show that genus one knots cannot yield Seifert fibered integral homology spheres with five or more singular fibers. Some other obstructions are also presented for higher genus knots.