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2010 A Schottky decomposition theorem for complex projective structures
Shinpei Baba
Geom. Topol. 14(1): 117-151 (2010). 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.

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Shinpei Baba. "A Schottky decomposition theorem for complex projective structures." Geom. Topol. 14 (1) 117 - 151, 2010. https://doi.org/10.2140/gt.2010.14.117

Information

Received: 27 May 2008; Accepted: 7 September 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1179.57025
MathSciNet: MR2578302
Digital Object Identifier: 10.2140/gt.2010.14.117

Subjects:
Primary: 57M50
Secondary: 30F40 , 53A30

Keywords: bending map , complex projective structure , measured lamination

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.14 • No. 1 • 2010
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