Local rigidity for PGL(3,C)-representations of 3-manifold groups

2013/07/31 by N. Bergeron, Nicolas Bergeron, E. Falbel +12
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.1307.8343

15 pages, 4 figures

arxiv created 2013/07/31 · openalex publication_date 2013/07/31 · arxiv updated 2013/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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