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
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
Views: 5950
Created: 30th Jan 2020 at 10:29
Last updated: 5th Mar 2024 at 21:24
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