A new computational tool for Khovanov cobordism maps

TL;DR

This paper introduces a Python tool for computing Khovanov cobordism maps, enabling detailed analysis of knot invariants and distinguishing ribbon disks for prime knots up to 10 crossings.

Contribution

The paper presents a novel computational Python module that calculates cobordism maps on Khovanov homology, expanding computational capabilities in knot theory.

Findings

Successfully computed cobordism maps for all incompressible Seifert surfaces of prime knots up to 10 crossings.

Distinguished many ribbon disks arising from symmetries of boundary knots.

Demonstrated the utility of the tool in analyzing knot invariants.

Abstract

We describe a Python module that we developed to calculate cobordism maps induced on Khovanov homology. As applications of our program, we compute these maps for all incompressible Seifert surfaces for prime knots up to 10 crossings, and distinguish many ribbon disks arising from symmetries of the boundary knots.