Year: 2015
Type: article
Abstract: 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 S via a natural projection of projective structures on S into Ᏻᏸ in Thurston coordinates.In a sequel paper, using this local solution, we prove the conjecture for generic holonomy.
Source: Geometry & Topology
Author: Shinpei Baba
Institution: Heidelberg University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2090593740