Geometry of the complex of curves and of Teichmueller space

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In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the complex of curves and the geometry of Teichmueller space.
17 pages, 2 figures; final version, to appear in "Handbook of Teichmueller theory"

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