Cable Links, Annuli and Sutured Floer homology

TL;DR

This paper uses sutured Floer homology to characterize and detect certain links and cables with specific Floer homology properties, providing new insights into link invariants and their detection capabilities.

Contribution

It introduces new characterizations of links with Floer homology matching certain cable links, enhancing link detection methods using sutured Floer homology.

Findings

Characterization of links with Floer homology similar to $(n,nm)$-cables of L-space knots.

Characterization of links with Floer homology similar to $(2,2m)$-cables of L-space knots.

New link detection results based on Floer homology properties.

Abstract

We apply sutured Floer homology techniques to study the knot and link Floer homologies of various links with annuli embedded in their exteriors. Our main results include, for large $m$, characterizations of links with the same link Floer homology as $(n,nm)$-cables of $L$-space knots or the same knot Floer homology as $(2,2m)$-cables of $L$-space knots. Note that Knot Floer homology carries less grading data than Link Floer homology, so the latter characterizations are stronger than former. These characterizations yield some new link detection results.