A scanning algorithm for odd Khovanov homology

TL;DR

This paper adapts a fast computational algorithm for even Khovanov homology to the odd variant, enabling efficient calculations and implementation for complex links, including 3-strand torus links.

Contribution

It introduces a novel adaptation of Bar-Natan's scanning algorithm for odd Khovanov homology using a mapping cone approach.

Findings

Successfully implemented the algorithm in software.

Computed odd Khovanov homology for 3-strand torus links.

Enhanced computational efficiency for odd Khovanov homology.

Abstract

We adapt Bar-Natan's scanning algorithm for fast computations in (even) Khovanov homology to odd Khovanov homology. We use a mapping cone construction instead of a tensor product, which allows us to deal efficiently with the more complicated sign assignments in the odd theory. The algorithm has been implemented in a computer program. We also use the algorithm to determine the odd Khovanov homology of 3-strand torus links.