New non-arithmetic complex hyperbolic lattices

Abstract

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.

References in corpus (1)

• Complex hyperbolic triangle groups

Cited by in corpus (14)

• On the convergence of arithmetic orbifolds
• A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
• A complex hyperbolic Riley slice
• Hybrid lattices and thin subgroups of Picard modular groups
• A new non-arithmetic lattice in PU(3,1)
• Lectures on complex hyperbolic Kleinian groups
• A uniformizable spherical CR structure on a two-cusped hyperbolic 3-manifold
• On bisectors in quaternionic hyperbolic space
• $\mathbb{C}$-Fuchsian subgroups of some non-arithmetic lattices
• Spherical CR uniformization of the magic 3-manifold
• Superrigidity, arithmeticity, normal subgroups: results, ramifications and directions
• Integral Gassman equivalence of algebraic and hyperbolic manifolds
• Hyperbolic 2-spheres with cone singularities
• Generators of the sister of Euclidean Picard modular group