On Heegaard Floer homology and Seifert fibered surgeries

Abstract

We explore certain restrictions on knots in the three-sphere which admit non-trivial Seifert fibered surgeries. These restrictions stem from the Heegaard Floer homology for Seifert fibered spaces, and hence they have consequences for both the Alexander polynomial of such knots, and also their knot Floer homology. In particular, we show that certain polynomials are never the Alexander polynomials of knots which admit homology three-sphere Seifert fibered surgeries. The knot Floer homology restrictions, on the other hand, apply also in cases where the Alexander polynomial gives no information, such as the Kinoshita-Terasaka knots.