Exploration of Andersen-Kashaev volume conjecture

Ben Aribi and Wong have described a combinatorial « FAMED » condition on an ideal triangulation of a knot complement under which Andersen-Kashaev volume conjecture holds.

I wrote a SageMath module « FAMEDexploration », that relies on Regina and Snappy, to try and explore how often this condition hold. It is available in this GitLab repository. The answer seems very clear: always for a hyperbolic knot complement!

Beware, there is a subtlety! We explored snappy’s census HTLinks for 42 136 knot complements with at most 14 crossings and at most 23 tetrahedra. For all but 6 cases, we find a triangulation (often not the one readily given by Snappy) that has the FAMED property, thus proving Andersen-Kashaev conjecture for as many examples.

A regina container containing all those triangulations is available here.