Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes

Details Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes

2011-03-24

arxiv.org/abs/1103.4674v1

Mathematics

Geometric Topology

37 pages - submitted to Handbook of Moduli (edited by G. Farkas and I. Morrison)

Scientific paper

Moduli spaces of hyperbolic surfaces may be endowed with a symplectic
structure via the Weil-Petersson form. Mirzakhani proved that Weil-Petersson
volumes exhibit polynomial behaviour and that their coefficients store
intersection numbers on moduli spaces of curves. In this survey article, we
discuss these results as well as some consequences and applications.

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