2010/03/03 by Young-Eun Choi, Choi, Young-Eun, David Dumas +3
Mathematics · #30F60 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #math.GT #msc:30F60
paper · pdf · doi:10.48550/arxiv.1003.0711
39 pages, 5 figures. v3: Minor corrections. v2: Main theorem improved using recent work of Rafi (arXiv:1011.6004), now compare rays from the same base point; introduction revised and sections reordered; many small corrections according to referee reports
openalex publication_date 2010/03/03 · arxiv created 2011/04/19 · arxiv updated 2011/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a measured geodesic lamination on a hyperbolic surface, grafting the surface along multiples of the lamination defines a path in Teichmuller space, called the grafting ray. We show that every grafting ray, after reparametrization, is a Teichmuller quasi-geodesic and stays in a bounded neighborhood of a Teichmuller geodesic. As part of our approach, we show that grafting rays have controlled dependence on the starting point. That is, for any measured geodesic lamination Lambda, the map of Teichmuller space which is defined by grafting along Lambda is L-Lipschitz with respect to the Teichmuller metric, where L is a universal constant. This Lipschitz property follows from an extension of grafting to an open neighborhood of Teichmuller space in the space of quasi-Fuchsian groups.