Homology of closed geodesics on hyperbolic manifolds with cusps

The presence of cusps in hyperbolic manifolds has an influence on the homol ogical behavior of closed geodesics. This phenomenon is studied here for a class of geometrically finite manifolds obtained as quotients of the hyperb olic space by free products of abelian groups acting in a Schottky way. We get in particular an exact estimate for the number of closed geodesics in a fixed homology class which depends in a peculiar way of the Hausdorff dime nsion of the limit set vith a transition at certain half-integer values. (C ) 2000 Editions scientifiques et medicales Elsevier SAS.