Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity

Elisha Falbel 1, 2, 3 Pierre-Vincent Koseleff 2, 3, 1 Fabrice Rouillier 2, 3, 1
1 UPMC - Université Pierre et Marie Curie - Paris 6
2 IMJ - Institut de Mathématiques de Jussieu
3 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
Inria Paris-Rocquencourt
Abstract : In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3;C) (in particular in PSL(2;C); PSL(3;R) and PU(2; 1)). The representations are obtained by gluing decorated tetrahedra of flags. We list complete computations (giving 0-dimensional or 1-dimensional solution sets) for the first complete hyperbolic non-compact manifolds with finite volume which are obtained gluing less than three tetrahedra with a description of the computer methods used to find them.
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https://hal.inria.fr/hal-00908843
Contributor : Fabrice Rouillier <>
Submitted on : Monday, November 25, 2013 - 1:42:42 PM
Last modification on : Sunday, March 31, 2019 - 1:43:46 AM

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Elisha Falbel, Pierre-Vincent Koseleff, Fabrice Rouillier. Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity. Geometriae Dedicata, Springer Verlag, 2015, 177 (1), pp.52. ⟨10.1007/s10711-014-9987-x⟩. ⟨hal-00908843⟩

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