Topology Seminar: Volume variation for representations of 3-manifold groups in SL_n(C)

Let M be a compact oriented three-manifold whose interior is hyperbolic of finite volume. In recent years the variety of representations of the fundamental group \pi_1(M) into semisimple Lie groups, most notably SL_2(C) and SL_n(C) has attracted a lot of attention. It turns out that many invariants of the variety M such as the volume, the Reidemeister torsion etc. can be extended to arbitrary representations. In this talk I will concentrate on the Volume of a representation and show, in case M has toric boundary, how we can derive a formula for the variation of the volume along a differentiable path in the variety of representations. This is joint work with J. Porti.