Complex Projective Structures
Differential Geometry
2009-02-12 v1
Abstract
This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the moduli space (2) Thurston's parameterization of the moduli space using grafting (3) Holonomy representations of CP^1 structures We also discuss some results comparing the two parameterizations of the space of projective structures and relating these parameterizations to the holonomy map.
Cite
@article{arxiv.0902.1951,
title = {Complex Projective Structures},
author = {David Dumas},
journal= {arXiv preprint arXiv:0902.1951},
year = {2009}
}
Comments
58 pages, 14 figures. To appear as a chapter in "Handbook of Teichmuller theory, volume II"