ar X iv : m at h / 05 05 24 4 v 1 [ m at h . G T ] 1 2 M ay 2 00 5 WORD HYPERBOLIC EXTENSIONS OF SURFACE GROUPS
نویسنده
چکیده
Let S be a closed surface of genus g ≥ 2. A finitely generated group Γ S is an extension of the fundamental group π 1 (S) of S if π 1 (S) is a normal subgroup of Γ S. We show that the group Γ S is hyperbolic if and only if the orbit map for the action of the quotient group Γ = Γ S /π 1 (S) on the complex of curves is a quasi-isometric embedding.
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