A Link Splitting Spectral Sequence in Khovanov Homology

TL;DR

This paper introduces a new spectral sequence in Khovanov homology that provides bounds on a link's splitting number and demonstrates that Khovanov homology can detect the unlink, advancing link invariants.

Contribution

It constructs a novel spectral sequence in Khovanov homology that bounds the splitting number and proves Khovanov homology detects the unlink.

Findings

Spectral sequence bounds the splitting number of links.

Khovanov homology detects the unlink.

Provides a new tool for link invariant analysis.

Abstract

We construct a new spectral sequence beginning at the Khovanov homology of a link and converging to the Khovanov homology of the disjoint union of its components. The page at which the sequence collapses gives a lower bound on the splitting number of the link, the minimum number of times its components must be passed through one another in order to completely separate them. In addition, we build on work of Kronheimer-Mrowka and Hedden-Ni to show that Khovanov homology detects the unlink.