Could somebody teach me about the relationship, if any, between hyperbolicity in groups (in Gromov sense) and hyperbolicity in 3-dimensional orbifolds? To be more specific, let Q be a 3-dimensional orbifold. If the orbifold fundamental group of Q is a hyperbolic group (in Gromov sense), then can we say that Q is a hyperbolic orbifold?
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Relationship between hyperbolicity in group theory and hyperbolicity in geometry
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