Jørgensen's inequality and collars in n-dimensional quaternionic hyperbolic space.
(2011)
Journal Article
Cao, W., & Parker, J. R. (2011). Jørgensen's inequality and collars in n-dimensional quaternionic hyperbolic space. The Quarterly Journal of Mathematics, 62(3), 523-543. https://doi.org/10.1093/qmath/haq003
Outputs (4)
Census of the complex hyperbolic sporadic triangle groups (2011)
Journal Article
Deraux, M., Parker, J. R., & Paupert, J. (2011). Census of the complex hyperbolic sporadic triangle groups. Experimental Mathematics, 20(4), 467-586. https://doi.org/10.1080/10586458.2011.565262The goal of this paper is to give a conjectural census of complex hyperbolic sporadic triangle groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and... Read More about Census of the complex hyperbolic sporadic triangle groups.
The geometry of the Gauss-Picard modular group (2011)
Journal Article
Falbel, E., Francsics, G., & Parker, J. R. (2011). The geometry of the Gauss-Picard modular group. Mathematische Annalen, 349(2), 459-508. https://doi.org/10.1007/s00208-010-0515-5We give a construction of a fundamental domain for PU(2,1,\mathbbZ [i])PU(21Z[i]), that is the group of holomorphic isometries of complex hyperbolic space with coefficients in the Gaussian ring of integers \mathbbZ [i]Z[i]. We obtain from that constr... Read More about The geometry of the Gauss-Picard modular group.
Generators of a Picard modular group in two complex dimensions (2011)
Journal Article
Falbel, E., Francsics, G., Lax, P. D., & Parker, J. R. (2011). Generators of a Picard modular group in two complex dimensions. Proceedings of the American Mathematical Society, 139, 2439-2447. https://doi.org/10.1090/s0002-9939-2010-10653-6The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space.... Read More about Generators of a Picard modular group in two complex dimensions.