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

Elisha Falbel; Pierre-Vincent Koseleff; Fabrice Rouillier

doi:10.1007/s10711-014-9987-x

Journal articles

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.

Document type :

Journal articles

Domain :

Mathematics [math] / Representation Theory [math.RT]

Mathematics [math] / Geometric Topology [math.GT]

Complete list of metadatas

https://hal.inria.fr/hal-00908843
Contributor : Fabrice Rouillier <>
Submitted on : Monday, November 25, 2013 - 1:42:42 PM
Last modification on : Wednesday, December 9, 2020 - 3:45:55 AM

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

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

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