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Quasifuchsian groups are a generalization of Fuchsian groups, representing discrete groups of isometries of hyperbolic 3-space that preserve a pair of disjoint, invariant Jordan curves on the sphere at infinity. These groups are significant in the study of Kleinian groups and Teichmüller theory, as they provide a rich structure connecting complex analysis, hyperbolic geometry, and low-dimensional topology.
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