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arXiv:1309.6010 [math.GT]AbstractReferencesReviewsResources

A birationality result for character varieties

Ben Klaff, Stephan Tillmann

Published 2013-09-24, updated 2015-08-19Version 2

Let M be an orientable, cusped hyperbolic 3-manifold of finite volume. We show that the restriction map from a Dehn surgery component in the PSL(2,C)-character variety of M to the character variety of the boundary of M is a birational isomorphism onto its image. This generalises a result by Nathan Dunfield. A key step in our proof is the exactness of Craig Hodgson's volume differential on the eigenvalue variety.

Comments: 8 pages; minor corrections in light of referee's comments; to appear in Mathematical Research Letters
Categories: math.GT
Subjects: 57M27
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