The orthospectra of finite volume hyperbolic manifolds with totally geodesic boundary

Geometry & Topology
Event time: 
Tuesday, February 16, 2010 - 11:30am to Monday, February 15, 2010 - 7:00pm
215 LOM
Martin Bridgeman
Event description: 

Given a finite volume hyperbolic n-manifold $M$ with totally geodesic boundary, an orthogeodesic of $M$ is a geodesic arc which is perpendicular to the boundary. For each dimension n, we show there is a real valued function $F_n$ such that the volume of any $M$ is the sum of values of $F_n$ on the orthospectrum (length of orthogeodesics). For $n=2$ the function $F_2$ is the Rogers L-function and the summation identities give dilogarithm identities on the Moduli space of surfaces.