Independent Loop Invariants for 2+1 Gravity

TL;DR

This paper identifies a complete set of Wilson loop invariants for 2+1 gravity on a three-manifold, utilizing Fenchel-Nielsen coordinates to facilitate the derivation.

Contribution

It provides an explicit, complete, and independent set of Wilson loop invariants for 2+1 gravity on a specific class of three-manifolds, using Teichmüller space coordinates.

Findings

Explicit Wilson loop invariants for 2+1 gravity derived.

Use of Fenchel-Nielsen coordinates in the derivation.

Complete and independent set of invariants identified.

Abstract

We identify an explicit set of complete and independent Wilson loop invariants for 2+1 gravity on a three-manifold $M=\R\times\Sigma^g$, with $\Sigma^g$ a compact oriented Riemann surface of arbitrary genus $g$. In the derivation we make use of a global cross section of the $PSU(1,1)$-principal bundle over Teichm\"uller space given in terms of Fenchel-Nielsen coordinates.