Weil-Petersson volumes and cone surfaces

2006/03/16 by Do, Norman, Norbury, Paul · 2 citations
#30F60 #32G15 #58D27 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0603406

Abstract

The moduli spaces of hyperbolic surfaces of genus g with n geodesic boundary components are naturally symplectic manifolds. Mirzakhani proved that their volumes are polynomials in the lengths of the boundaries by computing the volumes recursively. In this paper we give new recursion relations between the volume polynomials.

Cited by

• A q-analogue of Mirzakhani's recursion for Weil-Petersson volumes
• Topological gravity for arbitrary Dyson index

Related

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• Topological recursion of the Weil-Petersson volumes of hyperbolic surfaces with tight boundaries