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Complex projective structures with Schottky holonomy

Baba, Shinpei (2012) Complex projective structures with Schottky holonomy. Geometric and Functional Analysis, 22 (2). pp. 267-310. ISSN 1016-443X. doi:10.1007/s00039-012-0155-x.

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Let S be a closed orientable surface of genus at least two. Let Γ be a Schottky group whose rank is equal to the genus of S, and Ω be the domain of discontinuity of Γ. Pick an arbitrary epimorphism ρ : π_1(S) → Γ. Then Ω/Γ is a surface homeomorphic to S carrying a (complex) projective structure with holonomy ρ. We show that every projective structure with holonomy ρ is obtained by (2π-)grafting Ω/Γ along a multiloop on S.

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Additional Information:© 2012 Springer Basel AG. Received: February 2, 2009; Accepted: May 15, 2011.
Subject Keywords:Complex projective structure; grafting, Schottky group
Issue or Number:2
Classification Code:2010 Mathematics Subject Classification: Primary 57M50; Secondary 30F40, 20F65
Record Number:CaltechAUTHORS:20120712-093422747
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32376
Deposited By: Jason Perez
Deposited On:12 Jul 2012 17:43
Last Modified:09 Nov 2021 21:26

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