2 \pi-grafting and complex projective structures, I
Geometric Topology
2016-01-20 v5 Differential Geometry
Abstract
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.
Cite
@article{arxiv.1011.5051,
title = {2 \pi-grafting and complex projective structures, I},
author = {Shinpei Baba},
journal= {arXiv preprint arXiv:1011.5051},
year = {2016}
}
Comments
57 pages, 10 figures. To appear in Geometry & Topology