On the invariance of the Dowlin spectral sequence

TL;DR

This paper proves that the higher pages (from the third onward) of Dowlin's spectral sequence linking Khovanov homology and knot Floer homology are invariants of links, enhancing understanding of their relationship.

Contribution

It establishes the invariance of the $E_k$-pages for $k \,\geq\, 3$ in Dowlin's spectral sequence, which was previously unknown.

Findings

$E_k$-pages for $k\geq 3$ are link invariants.

Strengthens the connection between Khovanov and knot Floer homologies.

Provides new tools for link classification and invariants.

Abstract

Given a link $L$, Dowlin constructed a filtered complex inducing a spectral sequence with $E_2$-page isomorphic to the Khovanov homology $\overline{Kh}(L)$ and $E_\infty$-page isomorphic to the knot Floer homology $\widehat{HFK}(m(L))$ of the mirror of the link. In this paper, we prove that the $E_k$-page of this spectral sequence is also a link invariant, for $k\ge 3$.