Orthospectra of Geodesic Laminations and Dilogarithm Identities on Moduli Space

TL;DR

This paper establishes a connection between measured laminations on hyperbolic surfaces and dilogarithm identities on moduli space, revealing new summation formulas involving the Rogers dilogarithm.

Contribution

It introduces a measure derived from measured laminations that yields new dilogarithm identities on the moduli space of hyperbolic surfaces.

Findings

Derived a measure on the real line from measured laminations.

Established summation identities for the Rogers dilogarithm.

Connected geometric structures with special functions on moduli space.

Abstract

Given a measured lamination on a finite area hyperbolic surface we consider a natural measure Mon 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 gives summation identities for the Rogers dilogarithm function on the moduli space of a surface.