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arxiv: 1804.09840 · v2 · pith:BGXH6L65new · submitted 2018-04-26 · 🧮 math.GR · math.DG· math.GT

Geometric infiniteness in negatively pinched Hadamard manifolds

classification 🧮 math.GR math.DGmath.GT
keywords geometricallyinfinitecasediscretehadamardisometrymanifoldsnegatively
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We generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete isometry subgroups in the case of rank 1 symmetric spaces, and, under the assumption of bounded torsion, to the case of negatively pinched Hadamard manifolds. Every such geometrically infinite isometry subgroup $\Gamma$ has a set of nonconical limit points with cardinality of continuum.

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