Applications of Heegaard Floer Homology to Knot Concordance

Abstract

We consider several applications of Heegaard Floer homology to the study of knot concordance.

Using the techniques of bordered Heegaard Floer homology, we compute the concordance invariant $\tau$ for a family of satellite knots that generalizes Whitehead doubles.

We also construct an integer lift $\tilde\epsilon$ of the concordance invariant $\epsilon$. We introduce an interpretation of $\tilde\epsilon$ in terms of a filtration on $\cfhat(S^3_N K)$ induced by a family of knots $\mu_n \subset S^3_N K$.

Finally, we use truncated Heegaard Floer homology to construct a sequence of concordance invariants $\nu_n$ that generalizes previously known concordance invariants $\nu$, $\nu'$, and $\nu^+$.