Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes
Geometric Topology
2011-03-25 v1 Algebraic Geometry
Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1103.4674,
title = {Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes},
author = {Norman Do},
journal= {arXiv preprint arXiv:1103.4674},
year = {2011}
}
Comments
37 pages - submitted to Handbook of Moduli (edited by G. Farkas and I. Morrison)