Abstract
A spherical point of a Kleinian group Γ is a point of ℍ3 that is stabilized by a spherical triangle subgroup of Γ. Such points appear as vertices in the singular graph of the quotient hyperbolic 3-orbifold. We announce here sharp lower bounds for the hyperbolic distances between such points in H3. These bound from below the edge lengths of the singular graph. An elliptic element of a Kleinian group is simple if the translates of its axis under the group Γ form a disjoint collection of hyperbolic lines. Here we announce that the minimal covolume Kleinian group contains no simple elliptics of order p ≥ 3.
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