# Serre duality for Khovanov-Rozansky homology

## TL;DR

This paper proves that the full twist acts as a Serre functor in the homotopy category of type A Soergel bimodules, establishing a duality that relates Hochschild degrees in Khovanov-Rozansky homology.

## Contribution

It demonstrates that the full twist is a Serre functor in this category, linking Hochschild degrees and categorifying a known theorem.

## Key findings

- Full twist is a Serre functor in the homotopy category of type A Soergel bimodules
- Relates top and bottom Hochschild degrees in Khovanov-Rozansky homology
- Categorifies a theorem of Kálmán

## Abstract

We prove that the full twist is a Serre functor in the homotopy category of type A Soergel bimodules. As a consequence, we relate the top and bottom Hochschild degrees in Khovanov-Rozansky homology, categorifying a theorem of K\'alm\'an.