On the Dynamics of Pseudo-anosov Homeomorphisms on Representation Varieties of Surface Groups

We study the action of pseudo-Anosov homeomorphisms f : R → R on the character varieties of SL(2,C) -representations of the fundamental groups π1(R) of closed orientable hyperbolic surfaces R . We prove that the representation π1(R) →֒ SL(2,C) corresponding to the holonomy representation of the hyperbolic structure on the mapping torus of f is a hyperbolic fixed point for the action of f on the character variety X(π1(R)) .