2008/02/22 by Sebastian Hensel, Sebastian W. Hensel, Hensel, Sebastian W.
Computer Science · Mathematics · #30F60 #51M10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #msc:30F60 #msc:51M10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0802.3290
Major rewrite. Extended all of the results to multicurves and included a much more detailed treatment of holonomy lifts of both grafting rays and Teichmueller geodesics. 39 pages, 6 figures
openalex publication_date 2008/02/22 · arxiv created 2008/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a closed hyperbolic surface and λ, η be weighted geodesic multicurves which are short on X. We show that the iterated grafting along λ and η is close in the Teichmueller metric to grafting along a single multicurve which can be given explicitly in terms of λ and η. Using this result, we study the holonomy lifts grλρX,λ of Teichmueller geodesics ρX,λ for integral laminations λ and show that all of them have bounded Teichmueller distance to the geodesic ρX,λ. We obtain analogous results for grafting rays. Finally we consider the asymptotic behaviour of iterated grafting sequences \grnλX and show that they converge geometrically to a punctured surface.