Volume 19, issue 7 (2019)

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Four-genera of links and Heegaard Floer homology

Beibei Liu

Algebraic & Geometric Topology 19 (2019) 3511–3540
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.

Keywords
four-genus bounds, $L$–space links, $d$–invariants
Mathematical Subject Classification 2010
Primary: 57M25, 57M27