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

Kamiya, S.; Parker, J.R.

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.

Citation

Kamiya, S., & Parker, J. (2008). Discrete subgroups of PU(2,1) with screw parabolic elements. Mathematical Proceedings of the Cambridge Philosophical Society, 144(2), 443-455. https://doi.org/10.1017/s0305004107000941

• Journal Article Type: Article
• Publication Date: Mar 1, 2008
• Deposit Date: Nov 6, 2009
• Publicly Available Date: Nov 13, 2009
• Journal: Mathematical Proceedings of the Cambridge Philosophical Society
• Print ISSN: 0305-0041
• Electronic ISSN: 1469-8064
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 144
• Issue: 2
• Pages: 443-455
• DOI: https://doi.org/10.1017/s0305004107000941
• Public URL: https://durham-repository.worktribe.com/output/1547284