Complex Projective Structures
Abstract
This is a survey of the theory of complex projective (CP1) 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 CP1 structures We also discuss some results comparing the two parameterizations of the space of projective structures and relating these parameterizations to the holonomy map.
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