Complex Projective Structures

Details Complex Projective Structures Complex Projective Structures

2009-02-11

arxiv.org/abs/0902.1951v1

Mathematics

Differential Geometry

58 pages, 14 figures. To appear as a chapter in "Handbook of Teichmuller theory, volume II"

Scientific paper

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.

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