New non-arithmetic complex hyperbolic lattices

Martin Deraux (1) , John R. Parker (2) , Julien Paupert (3)

1 IF - Institut Fourier
2 Department of mathematical sciences
3 School of Mathematical and Statistical Sciences

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 fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete group acting on the complex hyperbolic plane.

Domaines: Topologie géométrique [math.GT]; Géométrie algébrique [math.AG]; Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Martin Deraux, John R. Parker, Julien Paupert. New non-arithmetic complex hyperbolic lattices. Inventiones Mathematicae, 2016, 203 (3), pp 681-771. ⟨10.1007/s00222-015-0600-1⟩. ⟨hal-00923014v2⟩