A survey of knot concordance invariants from Heegaard Floer homology
In this talk, we discuss several knot concordance invariants derived from Heegaard Floer homology. In particular, we focus on the correction terms of Dehn surgeries, Ni-Wu's V_k invariants and Hom-Wu's nu+ invariant.
A full-twist inequality for the nu+ invariant
Hom and Wu introduced a knot concordance invariant called nu+, which dominates many concordance invariants derived from Heegaard Floer homology. In this talk, we give a full-twist inequality for nu+. By using the inequality, we extend Wu's cabling formula for nu+ (which is proved only for particular positive cables) to all cables in the form of an inequality.
In addition, we also discuss nu+-equivalence, which is an equivalence relation on the knot concordance group. We introduce a partial order on nu+-equivalence classes, and study its relationship to full-twists.