A Theorem on Discrete, Torsion Free Subgroups of Isom H n
Let H n be the hyperbolic n-space with n⩾ 2. Suppose that Γ <Isom H n is a discrete, torsion free subgroup and a is a point in the domain of discontinuity Ω (Γ). Let p be the projection map from H n to the quotient manifold M=H n /Γ. In this paper we prove that there exists an open neighborhood U of a in H n ∪ Ω (Γ) such that p is an isometry on U∩ H n .
Keywordstorsion free subgroup domain of discontinuity
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