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

N. Bergeron; E. Falbel; A. Guilloux; P. -V. Koseleff; F. Rouillier

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arXiv · 1307.8343

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

N. Bergeron·E. Falbel·A. Guilloux·P. -V. Koseleff·F. Rouillier

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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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BibTeX RIS

N. Bergeron, E. Falbel, A. Guilloux, P. -V. Koseleff, F. Rouillier. 2013-07-31. Local rigidity for PGL(3,C)-representations of 3-manifold groups. https://arxiv.org/abs/1307.8343

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