Asymptotique de la norme
$L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique |
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Authors: | Nicolas Bergeron |
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Institution: | (1) Université Paris-Sud, Bat. 425, 91405 Orsay cedex, France (e-mail: Nicolas.Bergeron@math.u-psud.fr) , FR |
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Abstract: | Let M be an arithmetic hyperbolic manifold and be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the -norm of the lifts of F in the congruence tower above M. We obtain an explicit value for the growth rate of this norm. In particular, we provide a new proof of a celebrated result
of Millson Mi] on the homology of the arithmetic hyperbolic manifolds. The method is quite general and gives a new way of
getting non zero homology classes in certain locally symmetric spaces.
Received: 20 April 2001; in final form: 26 September 2001 / Published online: 28 February 2002 |
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Keywords: | Mathematics Subject Classification (2000):53C22 57R19 |
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