Foams and sl(n) cohomology for tangles (n > 3)

TL;DR

This paper introduces a new integral doubly-graded cohomology theory for tangles and links using foams and planar graphs, which categorifies the sl(n) polynomial for n > 3.

Contribution

It develops a novel foam-based cohomology framework that extends categorification of link invariants to higher sl(n) cases for n > 3.

Findings

Constructs an integral doubly-graded cohomology for tangles

Graded Euler characteristic matches the sl(n) link polynomial for n > 3

Provides a new categorification approach using foams and planar graphs

Abstract

We use 4-valent planar graphs and singular cobordisms (called foams) to construct an integral doubly-graded cohomology for tangles, and in particular for links, whose graded Euler characteristic yields the sl(n) link polynomial (for n > 3).