Invariants of 2+1 Quantum Gravity

TL;DR

This paper extends the algebraic understanding of 2+1 dimensional quantum gravity to arbitrary genus surfaces, analyzing the structure and center of the algebra of observables and classifying independent observables.

Contribution

It broadens previous work by systematically discussing the algebra's center and reducing the number of independent observables for higher genus surfaces.

Findings

Algebra of observables for 2+1 gravity extended to any genus.

Detailed classification of observables for genus 1 and 2.

Analysis of the algebra's center and reduction of independent observables.

Abstract

In [1,2] we established and discussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genus $g$ with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to $6g-6 (g > 1)$ is treated in detail with a precise classification for $g = 1$ and $g = 2$.