Orthospectra of Geodesic Laminations and Dilogarithm Identities 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.

21 pages, 2 figures

References in corpus (1)

• Chimneys, leopard spots, and the identities of Basmajian and Bridgeman

Cited by in corpus (11)

• The distribution of gaps for saddle connections on the octagon
• New Identities for small hyperbolic surfaces
• Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold
• Basmajian's identity in higher Teichmüller-Thurston theory
• Moments of a length function on the boundary of a hyperbolic manifold
• Quasiconformal homogeneity and subgroups of the mapping class group
• Poincaré series for surfaces with boundary
• On volumes of hyperideal tetrahedra with constrained edge lengths
• The Bridgeman-Kahn identity for hyperbolic manifolds with cusped boundary
• The Brownian loop measure on Riemann surfaces and applications to length spectra
• Linking numbers of modular knots