2 π-grafting and complex projective structures, I

Shinpei Baba

doi:10.2140/gt.2015.19.3233

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arXiv · 1011.5051

2 π-grafting and complex projective structures, I

Shinpei Baba

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Abstract

Let $S$ be a closed oriented surface of genus at least two. Gallo, Kapovich, and Marden asked if 2π-graftings produce all projective structures on $S$ with arbitrarily fixed holonomy (Grafting Conjecture). In this paper, we show that the conjecture holds true "locally" in the space $GL$ of geodesic laminations on $S$ via a natural projection of projective structures on $S$ into $GL$ in the Thurston coordinates. In the sequel paper, using this local solution, we prove the conjecture for generic holonomy.

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Shinpei Baba. 2016-01-10. 2 π-grafting and complex projective structures, I. https://doi.org/10.2140/gt.2015.19.3233

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