A dilogarithm identity on moduli spaces of curves
Feng Luo, Ser-Peow Tan
TL;DR
This paper proves a new dilogarithm identity related to the geometry of hyperbolic surfaces, involving lengths of geodesics in 3-holed spheres and 1-holed tori, contributing to the understanding of moduli spaces.
Contribution
It introduces a novel dilogarithm identity connecting geodesic lengths on hyperbolic surfaces, expanding the mathematical understanding of moduli spaces of curves.
Findings
Established a dilogarithm identity for hyperbolic surfaces
Connected geodesic lengths in 3-holed spheres and 1-holed tori
Enhanced understanding of moduli space structures
Abstract
We establish an identity for closed hyperbolic surfaces whose terms depend on the dilogarithms of the lengths of simple closed geodesics in all 3-holed spheres and 1-holed tori in the surface.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Algebraic Geometry and Number Theory