On p-adic propreties of the Witten-Reshetikhin-Turaev invariant

TL;DR

This paper proves that the trivial connection contribution to the Witten-Reshetikhin-Turaev invariant of rational homology spheres converges p-adicly, using properties of the Melvin-Morton expansion of the colored Jones polynomial, confirming a conjecture by R. Lawrence.

Contribution

It introduces a p-adic convergence proof for the trivial connection part of the Witten-Reshetikhin-Turaev invariant, based on the Melvin-Morton expansion.

Findings

Trivial connection contribution converges p-adicly to the invariant.

Confirms R. Lawrence's conjecture on p-adic convergence.

Links colored Jones polynomial properties to quantum invariants.

Abstract

We use the properties of the Melvin-Morton expansion of the colored Jones polynomial in order to prove that the trivial connection contribution converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant of rational homology spheres, as it was conjectured by R. Lawrence.