Volume 18, issue 1 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Branched projective structures with Fuchsian holonomy

Gabriel Calsamiglia, Bertrand Deroin and Stefano Francaviglia

Geometry & Topology 18 (2014) 379–446
Abstract

We prove that if S is a closed compact surface of genus g 2, 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.

Keywords
projective structures, fuchsian holonomy, moduli spaces
Mathematical Subject Classification 2010
Primary: 30F35, 57M20
Secondary: 53A30, 14H15
References
Publication
Received: 16 April 2012
Accepted: 30 May 2013
Published: 29 January 2014
Proposed: Benson Farb
Seconded: Yasha Eliashberg, Jean-Pierre Otal
Authors
Gabriel Calsamiglia
Instituto de Matemática
Universidade Federal Fluminense
Rua Mário Santos Braga s/n
24020-140, Niterói
Brazil
Bertrand Deroin
Département de mathématiques d’Orsay
Université Paris 11
91405 Orsay Cedex
France
Stefano Francaviglia
Dipartimento di Matematica
Università di Bologna
P.zza Porta S. Donato 5
40126 Bologna
Italy