2π–grafting and complex projective structures, I

Baba, Shinpei

doi:10.2140/gt.2015.19.3233

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

Shinpei Baba

Geometry & Topology 19 (2015) 3233–3287

DOI: 10.2140/gt.2015.19.3233

Abstract

Let $S$ be a closed oriented surface of genus at least two. Gallo, Kapovich and Marden asked whether $2 π$ –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 $G ℒ$ of geodesic laminations on $S$ via a natural projection of projective structures on $S$ into $G ℒ$ 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

Volume 19, issue 6 (2015)