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

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.

References in corpus (1)

• Deformation of hyperbolic manifolds in $\mathrm{PGL}(n,\mathbf{C})$ and discreteness of the peripheral representations

Cited by in corpus (5)

• A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
• Triangulation Independent Ptolemy Varieties
• A uniformizable spherical CR structure on a two-cusped hyperbolic 3-manifold
• Deformation space of discrete groups of SU(2,1) in quaternionic hyperbolic plane
• Volumes of representations and birationality of the peripheral holonomy