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Journal Articles Experimental Mathematics Year : 2018

Volume of representations and birationality of peripheral holonomy

Abstract

We discuss here a generalization of a theorem by Dun-field stating that the peripheral holonomy map, from the character variety of a 3-manifold to the A-polynomial is birational. Dun-field'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 computational experimentations are described, which support the conjecture.
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Dates and versions

hal-01370287 , version 1 (22-09-2016)

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Antonin Guilloux. Volume of representations and birationality of peripheral holonomy. Experimental Mathematics, 2018, 27 (4), ⟨10.1080/10586458.2017.1320240⟩. ⟨hal-01370287⟩
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