Abstract
The theorem, proved by Culler and Shalen, states that every point in the hyperbolic –space is moved a distance at least by one of the noncommuting isometries or of provided that and generate a torsion-free, discrete group which is not cocompact and contains no parabolic. This theorem lies in the foundations of many techniques that provide lower estimates for the volumes of orientable, closed hyperbolic –manifolds whose fundamental groups have no –generator subgroup of finite index and, as a consequence, gives insights into the topological properties of these manifolds.
Under the hypotheses of the theorem, the main result of this paper shows that every point in is moved a distance at least by one of the isometries , or .
Citation
İlker S Yüce. "Two-generator free Kleinian groups and hyperbolic displacements." Algebr. Geom. Topol. 14 (6) 3141 - 3184, 2014. https://doi.org/10.2140/agt.2014.14.3141
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