Lens Spaces and Handlebodies in 3D Quantum Gravity

TL;DR

This paper computes partition functions for lens spaces and handlebodies in 3D quantum gravity, providing explicit transition amplitudes within the Turaev-Viro framework for various topologies.

Contribution

It offers new explicit calculations of partition functions for lens spaces and handlebodies up to certain parameters in 3D quantum gravity.

Findings

Partition functions for lens spaces L_{p,q} up to p=8.

Partition functions for genus 1 and 2 handlebodies.

Interpretation of these functions as topological transition amplitudes.

Abstract

We calculate partition functions for lens spaces L_{p,q} up to p=8 and for genus 1 and 2 handlebodies H_1, H_2 in the Turaev-Viro framework. These can be interpreted as transition amplitudes in 3D quantum gravity. In the case of lens spaces L_{p,q} these are vacuum-to-vacuum amplitudes $\O -> \O$, whereas for the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological transition amplitudes $\O -> T^2$ and $\O -> T^2 # T^2$, respectively.