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2 \pi-grafting and complex projective structures, I
Let be a closed oriented surface of genus at least two. Gallo, Kapovich,
and Marden asked if 2\pi-graftings produce all projective structures on
with arbitrarily fixed holonomy (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 the Thurston coordinates. In the sequel paper, using this local
solution, we prove the conjecture for generic holonomy.Comment: 57 pages, 10 figures. To appear in Geometry & Topolog
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