# On the maximal degree of the Khovanov homology

## TL;DR

This paper demonstrates that the maximal homological degree of the Khovanov homology for a knot's cabling provides a lower bound for the knot's minimal positive crossing number, extending previous bounds.

## Contribution

It introduces a new lower bound for the minimal positive crossing number based on the Khovanov homology of a knot's cabling, expanding the applicability of homological invariants.

## Key findings

- Maximal homological degree of Khovanov homology bounds crossing number
- Cabling preserves the lower bound property
- Extends previous bounds to cabling knots

## Abstract

It is known that the maximal homological degree of the Khovanov homology of a knot gives a lower bound of the minimal positive crossing number of the knot. In this paper, we show that the maximal homological degree of the Khovanov homology of a cabling of a knot gives a lower bound of the minimal positive crossing number of the knot.