Volumes of SLn(C)–representations of hyperbolic 3–manifolds

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Let M be a compact oriented three-manifold whose interior is hyperbolic of finite volume. We prove a variation formula for the volume on the variety of representations of1 (M) in SLn (C). Our proof follows the strategy of Reznikov’s rigidity when M is closed; in particular, we use Fuks’s approach to variations by means of Lie algebra cohomology. When n = 2, we get Hodgson’s formula for variation of volume on the space of hyperbolic Dehn fillings. Our formula also recovers the variation of volume on the space of decorated triangulations obtained by Bergeron, Falbel and Guilloux and Dimofte, Gabella and Goncharov.

Original languageAmerican English
Pages (from-to)4067-4112
Number of pages46
JournalGeometry and Topology
Issue number7
Publication statusPublished - 6 Dec 2018

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