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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https://hal.archives-ouvertes.fr/hal-01370287
Contributor : Antonin Guilloux <>
Submitted on : Thursday, September 22, 2016 - 12:27:38 PM
Last modification on : Monday, June 3, 2019 - 9:20:02 AM

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  • HAL Id : hal-01370287, version 1
  • ARXIV : 1605.05917

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Antonin Guilloux. Volume of representations and birationality of peripheral holonomy. Experimental Mathematics, Taylor & Francis, 2017. ⟨hal-01370287⟩

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