2π–grafting and complex projective structures, I

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Abstract:

Let S be a closed oriented surface of genus at least two. Gallo, Kapovich and Marden asked whether 2\pi–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 \mathcalGL of geodesic laminations on S via a natural projection of projective structures on S into \mathcalGL in Thurston coordinates. In a sequel paper, using this local solution, we prove the conjecture for generic holonomy.

SEEK ID: https://publications.h-its.org/publications/996

DOI: 10.2140/gt.2015.19.3233

Research Groups: Groups and Geometry

Publication type: Journal

Journal: Geometry & Topology

Publisher: Mathematical Sciences Publishers

Citation: Geom. Topol. 19(6):3233-3287

Date Published: 2015

URL: http://dx.doi.org/10.2140/gt.2015.19.3233

Registered Mode: imported from a bibtex file

Author: Shinpei Baba

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Lukas Sauer

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Baba, S. (2015). 2π–grafting and complex projective structures, I. In Geometry & Topology (Vol. 19, Issue 6, pp. 3233–3287). Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2015.19.3233

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Created: 30th Jan 2020 at 10:29

Last updated: 5th Mar 2024 at 21:24

2π–grafting and complex projective structures, I

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