This repository contains various experiments computing the SU(2) version of the Turaev-Viro invariants of circle bundles over the once-punctured torus.
These notebooks contain a couple different implementations of algorithms for computing the Turaev-Viro invariants of the punctured torus bundles. One implementation uses the original definition of the invariant defined on a triangulation of the hyperbolic 3-manifold corresponding to each bundle, and the other implementation is a more efficient recursive formulation of the invariants from the perspective of quantum representations of the mapping class group of the punctured torus.
While these notebooks are not associated to any published research, their underlying theory is studied in the dissertation of Dr. Sanjay Kumar from MSU in 2021, where he gives a closed formula for the Turaev-Viro invariants of these manifolds, as well as in an informal collaborative research project between Sanjay and myself.
The code included here was written in part by both of us.
Sanjay Kumar and Joseph Melby April, 2021