A family of link concordance invariants from perturbed sl(n) homology

TL;DR

This paper introduces a new family of link concordance invariants derived from perturbed sl(n) homology, providing bounds on slice genus and splitting number, and generalizing existing knot invariants.

Contribution

It defines a new set of link invariants from perturbed sl(n) homology that extend Lobb's knot invariants to links, with applications to slice genus and splitting number.

Findings

Computed slice genus for positive links.

Provided lower bounds on link splitting number.

Determined splitting number for positive torus links.

Abstract

We define a family of link concordance invariants $\left\{ s_n \right\}_{n=2,3, \cdots}$. These link concordance invariants give lower bounds on the slice genus of a link $L$. We compute the slice genus of positive links. Moreover, these invariants give lower bounds on the link splitting number of a link. Especially, this new lower bound determines the splitting number of positive torus links. This is a generalization of Lobb's knot concordance invariants $\left\{ s_n \right\}$, obtained from Gornik's spectral sequence.