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

Kamiya, S.; Parker, J.R.

doi:10.1017/s0305004107000941

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

Kamiya, S.; Parker, J.R.

Authors

S. Kamiya

Professor John Parker j.r.parker@durham.ac.uk
Professor

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