Knot Floer homology, link Floer homology and link detection

Abstract

We give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T(2,4)$, $T(2,6)$, $T(3,3)$, $L7n1$, and the link $T(2,2n)$ with the orientation of one component reversed. We show link Floer homology detects $T(2,2n)$ and $T(n,n)$, for all $n$. Additionally we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology.

Theorems & Definitions (55)

• Theorem 3.1
• Theorem 3.2
• Lemma 3.3
• proof : Proof of Lemma \ref{['Unknot:KN']}
• proof : Proof of Theorem \ref{['HFK:KN']}
• Theorem 4.1
• Lemma 4.2
• Lemma 4.3
• proof
• proof : Proof of Lemma \ref{['HFKT24unknots']}