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$2\pi$–grafting and complex projective structures, I

Shinpei Baba

Geometry & Topology 19 (2015) 3233–3287
Abstract

Let S be a closed oriented surface of genus at least two. Gallo, Kapovich and Marden asked whether 2π–grafting produces all projective structures on S with arbitrarily fixed holonomy (the Grafting conjecture). In this paper, we show that the conjecture holds true “locally” in the space G of geodesic laminations on S via a natural projection of projective structures on S into G in Thurston coordinates. In a sequel paper, using this local solution, we prove the conjecture for generic holonomy.

Keywords
surface, complex projective structure, holonomy, grafting
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 30F40, 20H10
References
Publication
Received: 3 February 2014
Revised: 22 November 2014
Accepted: 26 January 2015
Published: 6 January 2016
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Danny Calegari
Authors
Shinpei Baba
Ruprecht-Karls-Universität Heidelberg
Mathematisches Institut
Im Neuenheimer Feld 368
Heidelberg, D-69120
Germany