# Homology of torus knots

## TL;DR

This paper provides an explicit formula for the triply graded Khovanov-Rozansky homology of any torus knot, confirming several existing conjectures in the field.

## Contribution

It introduces a new combinatorial approach using Elias-Hogancamp methods to compute homology for all torus knots, advancing the understanding of knot invariants.

## Key findings

- Explicit formula for homology of torus knots
- Verification of multiple conjectures in knot theory
- Enhanced computational methods for knot invariants

## Abstract

Using the method of Elias-Hogancamp and combinatorics of toric braids we give an explicit formula for the triply graded Khovanov-Rozansky homology of an arbitrary torus knot, thereby proving some of the conjectures of Aganagic-Shakirov, Cherednik, Gorsky-Negut and Oblomkov-Rasmussen-Shende.