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

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.

13 pages, 3 figures