Abstract
Let be a closed oriented surface of genus at least two. Gallo, Kapovich and Marden asked whether –grafting produces all projective structures on with arbitrarily fixed holonomy (the Grafting conjecture). In this paper, we show that the conjecture holds true “locally” in the space of geodesic laminations on via a natural projection of projective structures on into in Thurston coordinates. In a sequel paper, using this local solution, we prove the conjecture for generic holonomy.
Citation
Shinpei Baba. "$2\pi$–grafting and complex projective structures, I." Geom. Topol. 19 (6) 3233 - 3287, 2015. https://doi.org/10.2140/gt.2015.19.3233
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