Simpson's Theory and Superrigidity of Complex Hyperbolic Lattices

Details Simpson's Theory and Superrigidity of Complex Hyperbolic Lattices Simpson's Theory and Superrigidity of Complex Hyperbolic Lattices

1995-01-30

arxiv.org/abs/dg-ga/9501006v1

Mathematics

Differential Geometry

6 pages, plain TEX

Scientific paper

We attack a conjecture of J. Rogawski: any cocompact lattice in $S U (2, 1)$
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 $S L (3, \bbc)$.

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