Hyperbolic volume of representations of fundamental groups of cusped 3-manifolds
| dc.creator | Francaviglia, Stefano | |
| dc.date | 2003-05-19 | |
| dc.date.accessioned | 2026-07-07T04:58:07Z | |
| dc.date.available | 2026-07-07T04:58:07Z | |
| dc.description | Let W be a compact manifold and let ρbe a representation of its fundamental group into PSL(2,C). The volume of ρis defined by taking any ρ-equivariant map from the universal cover of W to H^3 and then by integrating the pull-back of the hyperbolic volume form on a fundamental domain. It turns out that such a volume does not depend on the choice of the equivariant map. Dunfield extended this construction to the case of a non-compact (cusped) manifold M, but he did not prove the volume is well-defined in all cases. We prove here that the volume of a representation is always well-defined and depends only on the representation. We show that this volume can be easily computed by straightening any ideal triangulation of M. We show that the volume of a representation is bounded from above by the relative simplicial volume of M. Finally, we prove a rigidity theorem for representations of the fundamental group of a hyperbolic manifold. Namely, we prove that if M is hyperbolic and vol(ρ)=vol(M) then ρis discrete and faithful. | |
| dc.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305275 | |
| dc.identifier | http://arxiv.org/abs/math/0305275 | |
| dc.identifier | A revised version is published: Int. Math. Res. Not., (9):425--459, 2004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67511 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50 | |
| dc.title | Hyperbolic volume of representations of fundamental groups of cusped 3-manifolds | |
| dc.type | text |