A condition on the Khovanov homology of three families of positive links

TL;DR

This paper extends previous bounds on the Jones polynomial to establish diagram-independent upper bounds on the quantum degree of Khovanov homology for three families of positive links, providing a new positivity obstruction.

Contribution

It introduces novel diagram-independent upper bounds on the Khovanov homology of specific positive link families, expanding the understanding of link invariants.

Findings

Established upper bounds on Khovanov homology degrees.

Provided a new positivity obstruction for positive links.

Extended previous Jones polynomial bounds to Khovanov homology.

Abstract

In previous work, we developed diagram-independent upper bounds on the maximum degree of the Jones polynomial of three families of positive links. These families are characterized by the second coefficient of the Jones polynomial. In this paper, we extend those results and construct diagram-independent upper bounds on the maximum non-vanishing quantum degree of the Khovanov homology of three families of positive links. This can be used as a positivity obstruction.