# A quantum categorification of the Alexander polynomial

## TL;DR

This paper introduces a new quantum categorification of the Alexander polynomial using foam evaluation, providing an algebraic version that links to existing triply graded link homology theories.

## Contribution

It presents a novel foam-based categorification method and an algebraic formulation connecting to Khovanov--Rozansky homology, advancing knot invariant theories.

## Key findings

- Categorification of Alexander polynomial via foam evaluation
- Algebraic version as infinite page of a spectral sequence
- Connection to reduced triply graded link homology

## Abstract

Using a modified foam evaluation, we give a categorification of the Alexander polynomial of a knot. We also give a purely algebraic version of this knot homology which makes it appear as the infinite page of a spectral sequence starting at the reduced triply graded link homology of Khovanov--Rozansky.