Local Rigidity for -Representations of 3-Manifold Groups

Nicolas Bergeron, Elisha Falbel, Antonin Guilloux, Pierre-Vincent Koseleff, Fabrice Rouillier

Type: Article

Publication Date: 2013-10-02

Citations: 12

DOI: https://doi.org/10.1080/10586458.2013.832441

Abstract

Let M be a noncompact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetrahedra. We explain how to produce local coordinates for the variety defined by the gluing equations for -representations. In particular, we prove local rigidity of the “geometric” representation in , recovering a recent result of Menal-Ferrer and Porti. More generally, we give a criterion for local rigidity of -representations and provide detailed analysis of the figure-eight-knot sister manifold exhibiting the different possibilities that can occur.

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