Outputs (4)

Unfaithful complex hyperbolic triangle groups I: Involutions (2008)
Journal Article
Parker, J. R. (2008). Unfaithful complex hyperbolic triangle groups I: Involutions. Pacific Journal of Mathematics, 238(1), 145-169. https://doi.org/10.2140/pjm.2008.238.145

A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that... Read More about Unfaithful complex hyperbolic triangle groups I: Involutions.

Complex hyperbolic Fenchel-Nielsen coordinates (2008)
Journal Article
Parker, J., & Platis, I. (2008). Complex hyperbolic Fenchel-Nielsen coordinates. Topology (Oxford), 47(2), 101-135. https://doi.org/10.1016/j.top.2007.08.001

Let Σ be a closed, orientable surface of genus g. It is known that the representation variety of π1(Σ) has 2g−3 components of (real) dimension 16g−16 and two components of dimension 8g−6. Of special interest are the totally loxodromic, faithful (that... Read More about Complex hyperbolic Fenchel-Nielsen coordinates.

Discrete subgroups of PU(2,1) with screw parabolic elements (2008)
Journal Article
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

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 th... Read More about Discrete subgroups of PU(2,1) with screw parabolic elements.

Jorgensen's inequality for non-Archimedean metric spaces (2008)
Presentation / Conference Contribution
Armitage, J., & Parker, J. R. (2006, September). Jorgensen's inequality for non-Archimedean metric spaces. Presented at Geometry and dynamics of groups and spaces : in memory of Alexander Reznikov., Bonn, Germany

Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. In this paper we generalise this to the case of groups of Möbius transformations of a non-Archimedean metric space. As an applicat... Read More about Jorgensen's inequality for non-Archimedean metric spaces.