61 citations · 81 across the 13 of their papers we have counts for
13 papers · 1 filter
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.
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.
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…
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…