Rigidity of representations in SO(4,1) for Dehn fillings on 2-bridge knots

Stefano Francaviglia, Joan Porti

Published 2007-12-10, updated 2008-08-01Version 2

We prove that, for a hyperbolic two bridge knot, infinitely many Dehn fillings are rigid in $SO_0(4,1)$. Here rigidity means that any discrete and faithful representation in $SO_0(4,1)$ is conjugate to the holonomy representation in $SO_0(3,1)$. We also show local rigidity for almost all Dehn fillings.