Outputs (3)

Cone metrics on the sphere and Livne's lattices (2006)
Journal Article
Parker, J. R. (2006). Cone metrics on the sphere and Livne's lattices. Acta Mathematica, 196(1), 1-64. https://doi.org/10.1007/s11511-006-0001-9

We give an explicit construction of a family of lattices in PU (1, 2) originally constructed by Livné. Following Thurston, we construct these lattices as the modular group of certain Euclidean cone metrics on the sphere. We give connections between t... Read More about Cone metrics on the sphere and Livne's lattices.

Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space (2006)
Journal Article
Parker, J. R., & Platis, I. D. (2006). Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space. Journal of Differential Geometry, 73(2), 319-350

Let pi(1), be the fundamental group of a closed surface Sigma of genus g > 1. One of the fundamental problems in complex hyperbolic geometry is to find all discrete, faithful, geometrically finite and purely loxodromic representations of pi(1) into S... Read More about Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space.

The geometry of the Eisenstein-Picard modular group (2006)
Journal Article
Falbel, E., & Parker, J. R. (2006). The geometry of the Eisenstein-Picard modular group. Duke Mathematical Journal, 131(2), 249-289. https://doi.org/10.1215/s0012-7094-06-13123-x

The Eisenstein-Picard modular group ${\rm PU}(2,1;\mathbb {Z}[\omega])$ is defined to be the subgroup of ${\rm PU}(2,1)$ whose entries lie in the ring $\mathbb {Z}[\omega]$, where $\omega$ is a cube root of unity. This group acts isometrically and pr... Read More about The geometry of the Eisenstein-Picard modular group.