Heegaard Floer Homology and Link Detection

Abstract

Heegaard Floer homology is a family of invariants in low dimensional topology due originally to Ozsváth-Szabó. We discuss various aspects of Heegaard Floer homology and give several link detection results for versions of Heegaard Floer homology for links. In particular, we show that knot and link Floer homology detect various infinite families of cable links. We also give classification results for the Heegaard Floer theoretic invariants of a type of knot called an “almost L-space knot” and an infinite family of detection results for annular Khovanov homology.