Volume of Representations and Birationality of Peripheral Holonomy. Issue 4 (2nd October 2018) - Guilloux, Antonin
ABSTRACT: A theorem by Dunfield states that the peripheral holonomy map from the SL(2, C )-character variety of a 3-manifold to the A-polynomial is a birational isomorphism. We discuss here a possible generalization to SL(n, C )-character varieties. Dunfield's proof involves the rigidity of maximal volume representations and the abundance of hyperbolic Dehn fillings. It is not directly transposable to the SL(n, C )-setting. In this article, we state a conjecture about the volume function on SL(n, C )-character varieties and prove it would imply the generalized birationality result. Some computational experimentations are also described, which support the conjecture.