Heegaard Floer homology of $L$-space links with two components

Beibei Liu

Vol. 298 (2019), No. 1, 83–112

DOI: 10.2140/pjm.2019.298.83

Abstract

We compute different versions of link Floer homology ${HFL}^{-}$ and $\widehat{HFL}$ for any $L$-space link with two components. The main approach is to compute the $h$-function of the filtered chain complex which is determined by Alexander polynomials of all sublinks of the $L$-space link. As an application, the Thurston norm of its complement is explicitly determined by Alexander polynomials of the link and its components.

Keywords

$L$-space links, link Floer homology, Thurston polytopes

Mathematical Subject Classification 2010

Primary: 57M99

Milestones

Received: 9 May 2017

Revised: 9 February 2018

Accepted: 23 March 2018

Published: 2 February 2019