An infinite torus braid yields a categorified Jones-Wenzl projector

TL;DR

This paper demonstrates that a sequence of categorification complexes for torus braids converges to a limit that can serve as a categorification of the Jones-Wenzl projector, linking braid theory and categorification.

Contribution

It introduces a new categorification approach for the Jones-Wenzl projector using infinite torus braids and their associated complexes.

Findings

Sequence of categorification complexes converges to a limit.

Limit serves as a categorification of the Jones-Wenzl projector.

Connects braid theory with categorification of quantum invariants.

Abstract

A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.