Transformation Groups and Moduli Spaces of Curves (volume 16 of the Advanced Lectures in Mathematics series)

Transformation groups have played a fundamental role in many areas of mathematics such as differential geometry, geometric topology, algebraic topology, algebraic geometry, and number theory. One of the basic reasons for their importance is that symmetries are described by groups (or rather, by group actions). Quotients of smooth manifolds by group actions are usually not smooth manifolds. On the other hand, if the actions of the groups are proper, then the quotients are orbifolds. An important example is given by the action of the mapping class groups on Teichmuller spaces: The quotients give the moduli spaces of Riemann surfaces (or algebraic curves) and are orbifolds... This volume consists of expanded lecture notes from two summer schools given in 2008: 'Transformation Groups and Orbifolds' and 'Geometry of Teichmuller Spaces and Moduli Spaces.' It should be a valuable source for study of transformation groups, orbifolds, Teichmuller spaces, mapping class groups, moduli spaces of curves, and related topics.