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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.


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.

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Record Created:06 Nov 2009 11:50
Last Modified:29 Nov 2011 13:18

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