Khovanov homology of a unicolored B-adequate link has a tail

TL;DR

This paper demonstrates that the Khovanov homology of a unicolored B-adequate link exhibits a stable tail, extending the known tail stability of the Jones polynomial to a categorified homological setting.

Contribution

The authors establish the existence of a stable tail in the Khovanov homology for unicolored B-adequate links, categorifying the tail stability of the Jones polynomial.

Findings

Khovanov homology of unicolored B-adequate links has a stable tail.

The graded Euler characteristic of this tail matches the Jones polynomial tail.

Extends polynomial tail stability results to a homological categorification.

Abstract

C. Armond, S. Garoufalidis and T.Le have shown that a unicolored Jones polynomial of a B-adequate link has a stable tail at large colors. We categorify this tail by showing that Khovanov homology of a unicolored link also has a stable tail, whose graded Euler characteristic coincides with the tail of the Jones polynomial.