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.
