Lens Spaces and Handlebodies in 3D Quantum Gravity

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 $Ø-> Ø$, whereas for the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological transition amplitudes $Ø-> T^2$ and $Ø-> T^2 # T^2$, respectively.