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Discrete subgroups of PU(2,1) with screw parabolic elements.

Kamiya, S. and Parker, J. R. (2008) 'Discrete subgroups of PU(2,1) with screw parabolic elements.', Mathematical proceedings of the Cambridge Philosophical Society., 144 (2). pp. 443-455.

Abstract

We give a version of Shimizu's lemma for groups of complex hyperbolic isometries one of whose generators is a parabolic screw motion. Suppose that G is a discrete group containing a parabolic screw motion A and let B be any element of G not fixing the fixed point of A. Our result gives a bound on the radius of the isometric spheres of B and B−1 in terms of the translation lengths of A at their centres. We use this result to give a sub-horospherical region precisely invariant under the stabiliser of the fixed point of A in G.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1017/S0305004107000941
Date accepted:No date available
Date deposited:13 November 2009
Date of first online publication:March 2008
Date first made open access:No date available

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