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Mathematics > Geometric Topology

arXiv:0710.4569 (math)
[Submitted on 24 Oct 2007 (v1), last revised 28 Dec 2010 (this version, v2)]

Title:A Schottky decomposition theorem for complex projective structures

Authors:Shinpei Baba
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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.
Comments: 35 pages, 14 figures
Subjects: Geometric Topology (math.GT); Differential Geometry (math.DG)
Cite as: arXiv:0710.4569 [math.GT]
  (or arXiv:0710.4569v2 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.0710.4569
Journal reference: Geometry & Topology 14 (2010) 117-151

Submission history

From: Shinpei Baba [view email]
[v1] Wed, 24 Oct 2007 21:12:12 UTC (417 KB)
[v2] Tue, 28 Dec 2010 09:36:55 UTC (418 KB)
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