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

## TL;DR

This paper computes various versions of link Floer homology for two-component L-space links, using Alexander polynomials to explicitly determine topological invariants like the Thurston polytope and norm.

## Contribution

It introduces a method to compute link Floer homology for two-component L-space links based on Alexander polynomials, providing explicit topological invariants.

## Key findings

- Explicit formulas for link Floer homology of 2-component L-space links.
- Determination of Thurston polytope and norm from Alexander polynomials.
- Method applicable to all 2-component L-space links.

## 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 the Alexander polynomials of every sublink of the $L$-space link. As an application, Thurston polytope and Thurston norm of any 2-component $L$-space link are explicitly determined by Alexander polynomials of the link and the link components.