  This paper compares two invariants of foliated manifolds which seem to
measure the non-Hausdorffness of the leaf space: the transversal length on the
fundamental group and the foliated Gromov norm on the homology. We consider
foliations with the property that the set of singular simplices transverse to
the foliation satisfies a weakened version of the Kan extension property. (We
prove that this assumption is fairly general: it holds for all
fibration-covered foliations, in particular for all foliations of 3-manifolds
without Reeb components.) For such foliations we show that vanishing of the
transversal length implies triviality of the foliated Gromov norm, and, more
generally, that uniform bounds on the transversal length imply explicit bounds
for the foliated Gromov norm.
