Volume of Representations and Birationality of Peripheral Holonomy. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Guilloux, Antonin
• Is Part Of: Experimental mathematics. Volume 27:Issue 4(2018)
• Page Start: 472
• Page End: 477
• Publication Date: 2018-10-02
• Subjects: character varieties -- volume; 57M27; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2017.1320240
• Languages: English
• ISSNs: 1058-6458

Abstract

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.