On the sl(2) foam cohomology computations

TL;DR

This paper introduces an efficient computational method for universal sl(2) foam cohomology groups using a divide and conquer approach, and presents a dotless topological version of the theory.

Contribution

It adapts Bar-Natan's divide and conquer technique for efficient computations and develops a purely topological, dotless sl(2) foam theory.

Findings

Efficient computation of sl(2) foam cohomology for large knots and links.

Development of a dotless, topological version of the foam theory.

Validation of the method's effectiveness on complex examples.

Abstract

We show how to use Bar-Natan's `divide and conquer' approach to computations to efficiently compute the universal sl(2) dotted foam cohomology groups, even for big knots and links. We also describe a purely topological version of the sl(2) foam theory, in the sense that no dots are needed on foams.