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

Research output: Contribution to journalArticleResearch


© 2018, Mathematical Sciences Publishers. All rights reserved. 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 languageEnglish
Pages (from-to)4067-4112
JournalGeometry and Topology
Publication statusPublished - 6 Dec 2018


Dive into the research topics of 'Volumes of SL_n(C)–representations of hyperbolic 3–manifolds'. Together they form a unique fingerprint.

Cite this