Local rigidity for SL (3,C) representations of 3-manifolds groups

Abstract : Let M be a non-compact hyperbolic 3-manifold that has a tri- angulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for SL(3, C)- representations. In particular we prove local rigidity of the "geometric" rep- resentation in SL(3, C), recovering a recent result of Menal-Ferrer and Porti. More generally we give a criterion for local rigidty of SL(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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Submitted on : Saturday, March 23, 2013 - 1:38:32 PM
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Nicolas Bergeron, Antonin Guilloux, Elisha Falbel, Pierre-Vincent Koseleff, Fabrice Rouillier. Local rigidity for SL (3,C) representations of 3-manifolds groups. Experimental Mathematics, Taylor & Francis, 2013, 22 (4), pp.10. ⟨10.1080/10586458.2013.832441⟩. ⟨hal-00803837⟩

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