Graded Bridgeman dilogarithm identities on hyperbolic surfaces

TL;DR

This paper extends Bridgeman's dilogarithm identity to hyperbolic cone surfaces with cusps and cone points, offering new tools for analyzing orthogeodesics on such surfaces.

Contribution

It introduces graded versions of Bridgeman's identity applicable to a broader class of hyperbolic surfaces with singularities.

Findings

Extended dilogarithm identities to cone surfaces with cusps and cone points

Provided applications to orthogeodesic analysis on hyperbolic surfaces

Enhanced understanding of hyperbolic surface invariants

Abstract

We establish graded versions of Bridgeman's dilogarithm identity for hyperbolic cone surfaces, including surfaces with only cusps and cone points, and provide applications to the study of orthogeodesics.