The Pressure metric for convex Anosov representations

Martin Bridgeman (Boston College)

Abstract: Using thermodynamics formalism, we introduce a notion of intersection for convex Anosov representations. We also produce an Out-invariant Riemannian metric on the smooth points of the deformation space of convex, irreducible representations of a word hyperbolic group G into SL(m,R) whose Zariski closure contains a generic element. In particular, we produce a mapping class group invariant Riemannian metric on Hitchin components which restricts to the Weil–Petersson metric on the Fuchsian locus.