Simpson's Theory and Superrigidity of Complex Hyperbolic Lattices

Abstract

We attack a conjecture of J. Rogawski: any cocompact lattice in $SU(2,1)$ for which the ball quotient $X=B^2/\Gamma$ satisfies $b_1(X)=0$ and $H^{1, 1} (X) \cap H^2 (X, \bbq) \approx \bbq$ is arithmetic. We prove the Archimedian suprerigidity for representation of $\Gamma$ is $S L (3, \bbc)$.

6 pages, plain TEX

Cited by in corpus (1)

• Finite subgroups of arithmetic lattices in U(2,1)