Abstract
ABSTRACTA 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.
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