On Heegaard Floer homology and Seifert fibered surgeries

摘要

We explore certain restrictions on knots in the three-sphere which admitnon-trivial Seifert fibered surgeries. These restrictions stem from theHeegaard Floer homology for Seifert fibered spaces, and hence they haveconsequences for both the Alexander polynomial of such knots, and also theirknot Floer homology. In particular, we show that certain polynomials are neverthe Alexander polynomials of knots which admit homology three-sphere Seifertfibered surgeries. The knot Floer homology restrictions, on the other hand,apply also in cases where the Alexander polynomial gives no information, suchas the Kinoshita-Terasaka knots.