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Hyperbolic spaces in Teichmüller spaces

Christopher J. LeiningerSaul Schleimer — 2014

Journal of the European Mathematical Society

We prove, for any n , that there is a closed connected orientable surface S so that the hyperbolic space n almost-isometrically embeds into the Teichmüller space of S , with quasi-convex image lying in the thick part. As a consequence, n quasi-isometrically embeds in the curve complex of S .

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