Outputs (5)

Complex hyperbolic free groups with many parabolic elements (2015)
Conference Proceeding
Parker, J. R., & Will, P. (2015). Complex hyperbolic free groups with many parabolic elements. In Geometry, groups and dynamics : ICTS program : groups, geometry and dynamics, December 3-16, 2012, Almora, India (327-348). https://doi.org/10.1090/conm/639/12782

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in PU(2,1) such that the boundary loops are mapped to PU(2,1) . We provide a system of coordinates on the corresponding representation variety, and ana... Read More about Complex hyperbolic free groups with many parabolic elements.

Traces in complex hyperbolic geometry (2012)
Conference Proceeding
Parker, J. R. (2012). Traces in complex hyperbolic geometry. In W. M. Goldman, C. Series, & S. P. Tan (Eds.), Geometry, topology and dynamics of character varieties (191-245). https://doi.org/10.1142/9789814401364_0006

We discuss the relationship between the geometry of complex hyperbolic manifolds and orbifolds and the traces of elements of the corresponding subgroup of SU(2, 1). We begin by showing how geometrical information about individual isometries is encode... Read More about Traces in complex hyperbolic geometry.

Complex hyperbolic quasi-Fuchsian groups (2010)
Conference Proceeding
Parker, J. R., & Platis, I. D. (2010). Complex hyperbolic quasi-Fuchsian groups. In F. P. Gardiner, G. González-Diez, & C. Kourouniotis (Eds.), Geometry of Riemann surfaces : proceedings of the Anogia conference to celebrate the 65th birthday of William J. Harvey (309-355)

Complex hyperbolic lattices (2009)
Conference Proceeding
Parker, J. R. (2009). Complex hyperbolic lattices. In K. Dekimpe, P. Igodt, & A. Valette (Eds.), Discrete groups and geometric structures: Workshop on Discrete Groups and Geometric Structures, with Applications III, May 26-30, 2008, Kortrijk, Belgium (1-42)

Jorgensen's inequality for non-Archimedean metric spaces (2008)
Conference Proceeding
Armitage, J., & Parker, J. R. (2008). Jorgensen's inequality for non-Archimedean metric spaces. In M. Kapranov, S. Kolyada, Y. Manin, P. Moree, & L. Potyagailo (Eds.), Geometry and dynamics of groups and spaces : in memory of Alexander Reznikov (97-111). https://doi.org/10.1007/978-3-7643-8608-5_2

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.