Geometry & Topology
- Geom. Topol.
- Volume 18, Number 1 (2014), 379-446.
Branched projective structures with Fuchsian holonomy
We prove that if is a closed compact surface of genus , and if is a quasi-Fuchsian representation, then the space of branched projective structures on with total branching order and holonomy is connected, for . 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 for non-elementary representations . It is shown to be a smooth complex manifold modeled on Hurwitz spaces.
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
Permanent link to this document
Digital Object Identifier
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]
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. https://projecteuclid.org/euclid.gt/1513732726