Volume of Representations and Birationality of Peripheral Holonomy

Antonin Guilloux
2017 Experimental Mathematics  
We discuss here a generalization of a theorem by Dunfield stating that the peripheral holonomy map, from the character variety of a 3-manifold to the A-polynomial is birational. Dunfield's proof involves the rigidity of maximal volume. The volume is still an important ingredient in this paper. Unfortunately at this point no complete proof is done. Instead, a conjecture is stated about the volume function on the character variety that would imply the generalized birationality result. Some
more » ... tional experimentations are described, which support the conjecture.
doi:10.1080/10586458.2017.1320240 fatcat:sjx52ibkkbcx5h5gccozi4n5kq