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

2013/07/25 by Elisha Falbel, Pierre-Vincent Koseleff, Falbel, E. +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1307.6697

openalex publication_date 2013/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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