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- Title
Asymptotique de la norme $L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique.
- Authors
Bergeron, Nicolas
- Abstract
Let M be an arithmetic hyperbolic manifold and $F\subset M$ be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the $L^2$ -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.
- Publication
Mathematische Zeitschrift, 2002, Vol 241, Issue 1, p101
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s002090100408