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

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.

Domaines: Théorie des représentations [math.RT]; Topologie géométrique [math.GT]

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, 2015, 177 (1), pp.52. ⟨10.1007/s10711-014-9987-x⟩. ⟨hal-00908843⟩