The foam and the matrix factorization sl3 link homologies are equivalent

TL;DR

This paper proves that two different constructions of universal rational sl3 link homologies, foam and matrix factorization, are fundamentally equivalent as functors from links to bigraded vector spaces.

Contribution

It establishes a natural isomorphism between foam and matrix factorization sl3 link homologies, unifying two approaches in the field.

Findings

Foam and matrix factorization homologies are naturally isomorphic.

The equivalence holds as projective functors from links to bigraded vector spaces.

Provides a unified framework for understanding sl3 link homologies.

Abstract

We prove that the foam and matrix factorization universal rational sl3 link homologies are naturally isomorphic as projective functors from the category of link and link cobordisms to the category of bigraded vector spaces.