Knot homology via derived categories of coherent sheaves II, sl(m) case

TL;DR

This paper introduces a new knot homology theory based on derived categories of equivariant coherent sheaves that categorifies the quantum sl(m) polynomial and aligns with existing homologies.

Contribution

It constructs a novel knot homology theory using geometric and categorical methods, conjecturally equivalent to Khovanov-Rozansky homology.

Findings

Satisfies categorified MOY relations

Conjecturally isomorphic to Khovanov-Rozansky homology

Links to geometric Satake and homological mirror symmetry

Abstract

Using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum sl(m) knot polynomial. Our knot homology naturally satisfies the categorified MOY relations and is conjecturally isomorphic to Khovanov-Rozansky homology. Our construction is motivated by the geometric Satake correspondence and is related to Manolescu's by homological mirror symmetry.