Knot Floer homology

Summary

Knot Floer homology is an invariant of knots in $3$-manifolds built from Heegaard Floer homology. It was introduced by Ozsváth and Szabó, and independently by Rasmussen. For a knot in $S^3$ it is a bigraded vector space whose graded Euler characteristic is the Alexander polynomial. It detects the Seifert genus of a knot and whether the knot is fibered.