English

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)