A short proof of the bounded geodesic image theorem

2013/01/25 by Richard C. H. Webb, Webb, Richard C. H.
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1301.6187

7 pages, 3 figures

arxiv created 2013/01/25 · arxiv updated 2013/01/29

Abstract

We give a combinatorial proof, using the hyperbolicity of the curve graphs, of the bounded geodesic image theorem of Masur and Minsky. Recently it has been shown that curve graphs are uniformly hyperbolic, thus a universal bound can be given for the diameter of the geodesic image. We also generalize the theorem for projections to markings of the whole surface.

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