Geometry & Topology

Branched projective structures with Fuchsian holonomy

Gabriel Calsamiglia, Bertrand Deroin, and Stefano Francaviglia

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We prove that if S is a closed compact surface of genus g2, and if ρ:π1(S) PSL(2,) is a quasi-Fuchsian representation, then the space k,ρ of branched projective structures on S with total branching order k and holonomy ρ is connected, for k>0. Equivalently, two branched projective structures with the same quasi-Fuchsian holonomy and the same number of branch points are related by a movement of branch points. In particular grafting annuli are obtained by moving branch points. In the appendix we give an explicit atlas for k,ρ for non-elementary representations ρ. It is shown to be a smooth complex manifold modeled on Hurwitz spaces.

Article information

Geom. Topol., Volume 18, Number 1 (2014), 379-446.

Received: 16 April 2012
Accepted: 30 May 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30F35: Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] 57M20: Two-dimensional complexes
Secondary: 53A30: Conformal differential geometry 14H15: Families, moduli (analytic) [See also 30F10, 32G15]

projective structures fuchsian holonomy moduli spaces


Calsamiglia, Gabriel; Deroin, Bertrand; Francaviglia, Stefano. Branched projective structures with Fuchsian holonomy. Geom. Topol. 18 (2014), no. 1, 379--446. doi:10.2140/gt.2014.18.379.

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