Filtrations on instanton homology

TL;DR

This paper demonstrates that the quantum and (co)homological gradings of Khovanov homology can be preserved as filtrations within the spectral sequence converging to instanton homology, extending the understanding of these invariants.

Contribution

The authors show how to realize quantum and (co)homological gradings as filtrations in the spectral sequence from Khovanov homology to instanton homology, providing new structural insights.

Findings

Gradings on Khovanov homology survive as filtrations

Spectral sequence abuts to instanton homology

Enhanced understanding of knot invariants

Abstract

In earlier work of the authors, the Khovanov complex of a knot or link appeared as the first page in a spectral sequence abutting to the instanton homology. The quantum and (co)homological gradings on Khovanov homology do not survive as gradings, but we show that they survive as filtrations.