On the first cohomology of arithmetic groups

Rajan, C. S. ; Venkataramana, T. N. (2001) On the first cohomology of arithmetic groups Manuscripta Mathematica, 105 (4). pp. 537-552. ISSN 0025-2611

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Official URL: http://www.springerlink.com/content/3jcr70dytn16gx...

Related URL: http://dx.doi.org/10.1007/s002290100196

Abstract

We study the restriction to smaller subgroups, of cohomology classes on arithmetic groups (possibly after moving the class by Hecke correspondences), especially in the context of first cohomology of arithmetic groups. We obtain vanishing results for the first cohomology of cocompact arithmetic lattices in SU(n,1) which arise from hermitian forms over division algebras D of degree p2, p an odd prime, equipped with an involution of the second kind. We show that it is not possible for a 'naive' restriction of cohomology to be injective in general. We also establish that the restriction map is injective at the level of first cohomology for non co-compact lattices, extending a result of Raghunathan and Venkataramana for co-compact lattices.

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ID Code:38325
Deposited On:29 Apr 2011 11:29
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