SO(3) quantum invariants are dense

TL;DR

This paper proves that for prime levels r ≥ 5, the SO(3) quantum invariants of three-manifolds are dense in the complex plane, confirming a conjecture and advancing understanding of quantum topology.

Contribution

It establishes the density of SO(3) quantum invariants for prime levels r ≥ 5, confirming a conjecture by Larsen and Wang.

Findings

SO(3) quantum invariants are dense in the complex plane for prime r ≥ 5

Confirms a conjecture of Larsen and Wang

Advances understanding of quantum invariants in topology

Abstract

We show that when $r \geq 5$ is prime, the SO(3) Witten-Reshetikhin-Turaev quantum invariants for three-manifolds at the level $r$ form a dense set in the complex plane. This confirms a conjecture of Larsen and Wang.