A discrete subgroup of , acting by Möbius transformations on the Riemann sphere or orientation-preserving isometries of hyperbolic space . A group may be Kleinian even when some elements fix points; freeness and absence of torsion are additional conditions.
A **Kleinian group** is a type of discontinuous group of isometries of hyperbolic 3-space (denoted as \(\mathbb{H}^3\)).
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