Truncated Heegaard Floer homology and knot concordance invariants

Abstract

We construct a sequence of smooth concordance invariants ${\nu }_n\left(K\right)$ defined using truncated Heegaard Floer homology. The invariants generalize the concordance invariants $\nu$ of Ozsváth and Szabó and ${\nu }^{+}$ of Hom and Wu. We exhibit an example in which the gap between two consecutive elements in the sequence ${\nu }_n$ can be arbitrarily large. We also prove that the sequence ${\nu }_n$ contains more concordance information than $\tau$, $\nu$, ${\nu }^{\prime }$, ${\nu }^{+}$ and ${\nu }^{{+}^{\prime }}$.