4 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…
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.