A Schottky decomposition theorem for complex projective structures

Baba, Shinpei

doi:10.2140/gt.2010.14.117

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A Schottky decomposition theorem for complex projective structures

Shinpei Baba

Geometry & Topology 14 (2010) 117–151

DOI: 10.2140/gt.2010.14.117

Abstract

Let $S$ be a closed orientable surface of genus at least two, and let $C$ be an arbitrary (complex) projective structure on $S$ . We show that there is a decomposition of $S$ into pairs of pants and cylinders such that the restriction of $C$ to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can be obtained by the construction of Gallo, Kapovich, and Marden. Along the way, we show that there is an admissible loop on $(S, C)$ , along which a grafting can be done.

Keywords

complex projective structure, bending map, measured lamination

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 30F40, 53A30

References

Publication

Received: 27 May 2008

Accepted: 7 September 2009

Preview posted: 10 October 2009

Published: 2 January 2010

Proposed: David Gabai

Seconded: Walter Neumann, Benson Farb

Authors

Shinpei Baba
Mathematisches Institut Universität Bonn 53115 Bonn Germany

Volume 14, issue 1 (2010)