Outputs (4)

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)

Unfaithful complex hyperbolic triangle groups II: Higher order reflections (2009)
Journal Article
Parker, J. R., & Paupert, J. (2009). Unfaithful complex hyperbolic triangle groups II: Higher order reflections. Pacific Journal of Mathematics, 239(2), 357-389. https://doi.org/10.2140/pjm.2009.239.357

We consider symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2π ∕ p, with p ≥ 3. We restrict our attention to those groups where certain words are elliptic. Our goal is to find necessary conditions for... Read More about Unfaithful complex hyperbolic triangle groups II: Higher order reflections.

Global, geometrical coordinates on Falbel's cross-ratio variety (2009)
Journal Article
Parker, J. R., & Platis, I. D. (2009). Global, geometrical coordinates on Falbel's cross-ratio variety. Canadian Mathematical Bulletin, 52(2), 285-294. https://doi.org/10.4153/cmb-2009-031-3

Falbel has shown that four pairwise distinct points on the boundary of a complex hyperbolic 2-space are completely determined, up to conjugation in PU(2,1), by three complex cross-ratios satisfying two real equations. We give global geometrical coord... Read More about Global, geometrical coordinates on Falbel's cross-ratio variety.

Conjugacy classification of quaternionic Möbius transformations (2009)
Journal Article
Parker, J. R., & Short, I. (2009). Conjugacy classification of quaternionic Möbius transformations. Computational Methods and Function Theory - Springer, 9(1), 13-25. https://doi.org/10.1007/bf03321711

It is well known that the dynamics and conjugacy class of a complex Möbius transformation can be determined from a simple rational function of the coefficients of the transformation. We study the group of quaternionic Möbius transformations and ident... Read More about Conjugacy classification of quaternionic Möbius transformations.