Spectral sequences in unoriented link Floer homology

TL;DR

This paper constructs a spectral sequence connecting Khovanov homology to unoriented link Floer homology, extending previous work with an iterative skein exact triangle, providing new tools for knot invariants analysis.

Contribution

It introduces a spectral sequence from various Khovanov homologies to unoriented link Floer homology, generalizing earlier skein triangle results.

Findings

Spectral sequence from Khovanov homology to link Floer homology for knots in S^3.

Extension of skein exact triangle to an iterative form.

Connection between reduced Khovanov homology of mirror knots and knot Floer homology.

Abstract

In a previous work, we defined an unoriented skein exact triangle in unoriented link Floer homology. In this paper, we iterate a modified version of this exact triangle and obtain a spectral sequence from various versions of Khovanov homology to various versions of unoriented link Floer homology, over the field with two elements. In particular, for knots in $S^{3}$, we obtain a spectral sequence from the reduced Khovanov homology of the mirror of the knot to the knot Floer homology of the knot.