Orthospectra of geodesic laminations and dilogarithm identities on moduli space

Abstract

Given a measured lamination $\lambda$ on a finite area hyperbolic surface we consider a natural measure $M_{\lambda }$ on the real line obtained by taking the push-forward of the volume measure of the unit tangent bundle of the surface under an intersection function associated with the lamination. We show that the measure $M_{\lambda }$ gives summation identities for the Rogers dilogarithm function on the moduli space of a surface.