Maximal representations of uniform complex hyperbolic lattices
نویسندگان
چکیده
منابع مشابه
Uniform Lattices Acting on Some Hyperbolic Buildings
Let X be a 2-dimensional right-angled hyperbolic building. We characterise the set of covolumes of uniform lattices in Aut(X). We also show that the group Aut(X) admits an infinite ascending tower of uniform lattices.
متن کاملNew non-arithmetic complex hyperbolic lattices
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 construc...
متن کاملCongruence Lattices of Uniform Lattices
A lattice L is uniform, if for any congruence Θ of L, any two congruence classes A and B of Θ are of the same size, that is, |A| = |B| holds. A classical result of R. P. Dilworth represents a finite distributive lattice D as the congruence lattice of a finite lattice L. We show that this L can be constructed as a finite uniform lattice.
متن کاملSimpson ’ s Theory and Superrigidity of Complex Hyperbolic Lattices
We attack a conjecture of J. Rogawski: any cocompact lattice in SU(2, 1) for which the ball quotient X = B/Γ satisfies b1(X) = 0 and H (X)∩H(X,Q) ≈ Q is arithmetic. We prove the Archimedian suprerigidity for representation of Γ is SL(3,C). Théorie de Simpson et superrigidité des réseaux hyperboliques complexes Résumé Soit Γ ⊂ SU(2, 1) un reseau cocompact et soit X = B/Γ. Nous preuvons: si b1(X)...
متن کاملLattices in Hyperbolic Buildings
This survey is intended as a brief introduction to the theory of hyperbolic buildings and their lattices. Hyperbolic buildings are negatively curved geometric objects which also have a rich algebraic and combinatorial structure, and the study of these buildings and the lattices in their automorphism groups involves a fascinating mixture of techniques from many different areas of mathematics. Ro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2017
ISSN: 0003-486X
DOI: 10.4007/annals.2017.185.2.3