Cable Links, Annuli and Sutured Floer homology

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 n, characterizations of links with the same link Floer homology as (m, mn)cables of L-space knots, or the same knot Floer homology as (2, 2n)-cables of L-space knots. These yield some new link detection results.