Transverse geodesic cycles in hyperbolic manifolds

Let M be a hyperbolic manifold, with pi(1)M finitely generated. Let c(1) and c(2) be two transverse geodesic cycles with dim(c(1)) + dim(c(2)) dim M and c(1) boolean AND c(2) not equal 0. In this paper, following ideas of [MR], we prove (Theorem 6) that c(1) and c(2) lifts to a finite cover of M as two submanifolds F-1 and F-2 with [F-1] I [F-2] not equal 0 This theorem implies in particular that the compact hyperbolic manifolds constructed by Gromov and Piatetski-Shapiro in [GP] have non-trivial virtual Betti numbers.