Four-genera of links and Heegaard Floer homology

Abstract

For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint oriented surfaces in $B^4$. We use the $h$–function which is a link invariant from the Heegaard Floer homology to give lower bounds for the $4$–genus of the link. For $L$–space links, the $h$–function is explicitly determined by the Alexander polynomials of the link and its sublinks. We show some $L$–space links where the lower bounds are sharp, and also describe all possible genera of disjoint oriented surfaces bounded by such links.