61 citations · 73 across the 11 of their papers we have counts for
13 papers
Complex hyperbolic surfaces whose closed geodesics are all simple
Sami Douba, D. B. McReynolds, Julien Paupert +1
We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Pra…
Parabolic-preserving deformations of cusped hyperbolic lattices
Samuel A. Ballas, Julien Paupert, Pierre Will
We study deformations of non-cocompact lattices of into and . A necessary condition for these deformations to remain discrete and f…
Nil 3-manifolds and cusps of complex hyperbolic surfaces
Julien Paupert, Connor Sell
McReynolds showed that every compact Nil 3-manifold occurs as the cusp cross-section of some arithmetic complex hyperbolic 2-manifold. We classify which commensurability classes of…
Complex hyperbolic and projective deformations of small Bianchi groups
Julien Paupert, Morwen Thistlethwaite
The Bianchi groups ${\rm Bi}(d)={\rm PSL}(2,\mathcal{O}_d) < {\rm PSL}(2,\C)$ (where denotes the ring of integers of $\Q (i\sqrt{d})$, with squarefr…
Picard modular groups generated by complex reflections
Alice Mark, Julien Paupert, David Polletta
In this short note we use the presentations found in \cite{MP} and \cite{Po} to show that the Picard modular groups with (respectively the q…
Hybrid lattices and thin subgroups of Picard modular groups
Julien Paupert, Joseph Wells
We consider a certain hybridization construction which produces a subgroup of from a pair of lattices in . Among the Picard modular groups ${\rm PU…
Presentations for cusped arithmetic hyperbolic lattices
Alice Mark, Julien Paupert
We present a general method to compute a presentation for any cusped arithmetic hyperbolic lattice , applying a classical result of Macbeath to a suitable -invariant horoball…
Rank 1 deformations of non-cocompact hyperbolic lattices
Samuel A. Ballas, Julien Paupert, Pierre Will
Let be a negatively curved symmetric space and a non-cocompact lattice in . We show that small, parabolic-preserving deformations of into the isometry gro…
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…
Involution and commutator length for complex hyperbolic isometries
Julien Paupert, Pierre Will
We study decompositions of complex hyperbolic isometries as products of involutions. We show that PU(2,1) has involution length 4 and commutator length 1, and that for all $n \geqs…
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…
Real reflections, commutators and cross-ratios in complex hyperbolic space
Julien Paupert, Pierre Will
We provide a concrete criterion to determine whether or not two given elements of PU(2,1) can be written as products of real reflections, with one reflection in common. As an appli…
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…