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ASYMPTOTIC SINGULAR HOMOLOGY OF A COMPLETE HYPERBOLIC 3-MANIFOLD OF FINITE VOLUME

Published online by Cambridge University Press:  01 September 1999

J. FRANCHI
J. FRANCHI
Affiliation:
Laboratoire de Probabilités de Paris 6, 4 place Jussieu, tour 56, 3ème étage, 75252 Paris cedex 05, France. Faculté des Sciences de Paris 12, 61 avenue de Gaulle, 94010 Créteil cedex, [email protected]
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Abstract

Let $\cal V$ be a complete connected hyperbolic 3-manifold of finite volume, with Liouville measure $m$, geodesic flow $\Gamma_t$ and Brownian motion $Z_t$. Let $\omega$ be a smooth 1-form, closed in the cusps of $\cal V$. Then the limit laws as $t \to \infty$ of $(t\log t)^{-1/2}\int_0^t\omega(\Gamma_s)$ under $m$ and of $(t\log t)^{-1/2}\int_0^t\omega(Z_s)$ are calculated, and seen to be Gaussian, and equal. The geodesic flow case is studied via the Brownian case.

1991 Mathematics Subject Classification: 60J65, 58F17, 51M10.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 2 , September 1999 , pp. 451 - 480
Copyright
1999 London Mathematical Society

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