Truncated Heegaard Floer Homology and Knot Concordance Invariants

TL;DR

This paper introduces a new sequence of integer-valued knot concordance invariants, generalizing existing invariants, to enhance the understanding of knot concordance in low-dimensional topology.

Contribution

The authors construct a sequence of invariants $ u_n(K)$ that extend the Ozsváth-Szabó $ u$-invariant and Hom-Wu $ u^+$-invariant, providing new tools for knot concordance analysis.

Findings

Defined a sequence of invariants $ u_n(K)$ for knots.

Proved these invariants generalize existing concordance invariants.

Potential applications in distinguishing knot concordance classes.

Abstract

In this paper we construct a sequence of integer-valued concordance invariants $\nu_n(K)$ that generalize the Ozsv\'ath-Szab\'o $\nu$-invariant and the Hom-Wu $\nu^+$-invariant.