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2<i>π</i>–grafting and complex projective structures, I

2<i>π</i>–grafting and complex projective structures, I

Let S be a closed oriented surface of genus at least two.Gallo, Kapovich and Marden asked whether 2 -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 Ᏻᏸ of geodesic laminations on …