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Almost-Bieberbach groups with prime order holonomy

Karel Dekimpe, Wim Malfait (1996)

Fundamenta Mathematicae

The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base.  In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...

An application of metric diophantine approximation in hyperbolic space to quadratic forms.

Sanju L. Velani (1994)

Publicacions Matemàtiques

For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...

Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Martine Babillot, Marc Peigné (2006)

Bulletin de la Société Mathématique de France

We consider a large class of non compact hyperbolic manifolds M = n / Γ with cusps and we prove that the winding process ( Y t ) generated by a closed 1 -form supported on a neighborhood of a cusp 𝒞 , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp 𝒞 and the Poincaré exponent δ of Γ . No assumption on the value of δ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.

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