Volumes of SL_n(C)-representations of hyperbolic 3-manifolds
Pitsch, Wolfgang (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Porti, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2018
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2016-80439-P Ministerio de Economía y Competitividad MTM2015-66165-P Ministerio de Economía y Competitividad MDM-2014-0445
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Geometry and Topology, Vol. 22, Issue 7 (December 2018) , p. 4067-4112, ISSN 1364-0380

DOI: 10.2140/gt.2018.22.4067

Postprint 32 p, 633.5 KB

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