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Simpson's Theory and Superrigidity of Complex Hyperbolic Lattices

Alexander Reznikov
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Abstract

We attack a conjecture of J. Rogawski: any cocompact lattice in $S U (2, 1)$ for which the ball quotient $X = B^2 / Γ$ 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 $Γ$ is $S L (3, \bbc)$.

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Alexander Reznikov. 1995-01-30. Simpson's Theory and Superrigidity of Complex Hyperbolic Lattices. https://arxiv.org/abs/dg-ga/9501006

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