61 citations · 81 across the 13 of their papers we have counts for
18 papers
On the type of a complex hyperbolic triangle group
Wei Liao, John R Parker
In this paper we consider groups of complex hyperbolic isometries generated by three complex involutions. Our first main result states that if the group is discrete and at least tw…
Minimising length of closed billiard trajectories on hyperbolic polygons
John Parker, Manvendra Somvanshi
In a hyperbolic polygon any finite collection of closed billiard trajectories can be assigned an average length function. In this paper, we consider the average length of the colle…
Fenchel-Nielsen coordinates for SL(3,C) representations
Rodrigo Dávila Figueroa, John R Parker
We define Fenchel-Nielsen coordinates for representations of surface groups to . We also show how these coordinates relate to the classical Fenchel-Nielsen…
Free groups generated by two parabolic maps
Sagar B. Kalane, John R. Parker
In this paper we consider a group generated by two unipotent parabolic elements of with distinct fixed points. We give several conditions that guarantee the group i…
Classification of non-free Kleinian groups generated by two parabolic transformations
Hirotaka Akiyoshi, Ken'ichi Ohshika, John Parker +2
We give a full proof to Agol's announcement on the classification of non-free Kleinian groups generated by two parabolic transformations.
Chaotic Delone sets
Jesús Antonio Álvarez López, Ramón Barral Lijó, John Hunton +2
We present a definition of chaotic Delone set, and establish the genericity of chaos in the space of -Delone sets for . We also present a hyperbolic analogue of the…
Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces
Gerhard Knieper, John R. Parker, Norbert Peyerimhoff
In this article we consider solvable hypersurfaces of the form with induced metrics in the symmetric space $M = SL(3,\C)/SU(3)$, where a suitable unit length vec…
Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type
Andrew Monaghan, John R. Parker, Anna Pratoussevitch
In this paper we consider ultra-parallel complex hyperbolic triangle groups of type , i.e. groups of isometries of the complex hyperbolic plane, generated by complex r…
Non-arithmetic monodromy of higher hypergeometric functions
John R. Parker
We show that all the currently known non-arithmetic lattices in are monodromy groups of higher hypergeometric functions.
Complex Hyperbolic Triangle Groups with 2-fold Symmetry
John R. Parker, Li-Jie Sun
In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will…
New non-arithmetic complex hyperbolic lattices II
Martin Deraux, John R. Parker, Julien Paupert
We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups, a class of groups that contains a representative of the commensurability clas…
Minimizing length of billiard trajectories in hyperbolic polygons
John R. Parker, Norbert Peyerimhoff, Karl Friedrich Siburg
Closed billiard trajectories in a polygon in the hyperbolic plane can be coded by the order in which they hit the sides of the polygon. In this paper, we consider the average lengt…
A complex hyperbolic Riley slice
John R. Parker, Pierre Will
We study subgroups of generated by two non-commuting unipotent maps and whose product is also unipotent. We call the set of conjugacy cla…
New non-arithmetic complex hyperbolic lattices
Martin Deraux, John R. Parker, Julien Paupert
We produce a family of new, non arithmetic lattices in PU(2,1). All previously known examples were commensurable with lattices constructed by Picard, Mostow and Deligne-Mostow, and…
Complex hyperbolic free groups with many parabolic elements
John R. Parker, Pierre Will
We consider in this work representations of the of the fundamental group of the 3-punctured sphere in such that the boundary loops are mapped to . We…
Census of the complex hyperbolic sporadic triangle groups
Martin Deraux, John R. Parker, Julien Paupert
The goal of this paper is to give a conjectural census of complex hyperbolic sporadic groups. We prove that only finitely many of these sporadic groups are lattices. We also give a…
Jorgensen's Inequalities and Collars in n-dimensional Quaternionic Hyperbolic Space
Wensheng Cao, John R. Parker
In this paper, we obtain analogues of Jorgensen's inequality for non-elementary groups of isometries of quaternionic hyperbolic -space generated by two elements, one of which is…
Coordinates for quasi-Fuchsian punctured torus space
John R. Parker, Jouni Parkkonen
We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are…