On the link Floer homology of $L$-space links

TL;DR

This paper proves that for 2- or 3-component L-space links, the link Floer homology is fully determined by the Alexander polynomial of sub-links and linking numbers, and classifies all 2-bridge L-space links.

Contribution

It establishes a complete determination of link Floer homology for certain L-space links and classifies all 2-bridge L-space links using these invariants.

Findings

HFL^- is determined by Alexander polynomials and linking numbers for 2- or 3-component L-space links.

Provides restrictions on the multi-variable Alexander polynomial of L-space links.

Classifies all 2-bridge L-space links.

Abstract

We will prove that, for a $2$ or $3$ component $L$-space link, $HFL^-$ is completely determined by the multi-variable Alexander polynomial of all the sub-links of $L$, as well as the pairwise linking numbers of all the components of $L$. We will also give some restrictions on the multi-variable Alexander polynomial of an $L$-space link. Finally, we use the methods in this paper to prove a conjecture by Yajing Liu classifying all $2$-bridge $L$-space links.