A VIRTUAL LEAF

Abstract

First, we study the growth rate of separation of pseudo-orbits of a finitely generated group acting on a compact space. Then, suspending a suitable group action and a suitable pseudo-orbit we get, after a minor modification, a foliation and a Riemannian manifold which is not quasi-isometric to any leaf of any compact foliated manifold but which is quasi-isometric to pseudoleaves of the constructed foliation intersecting its leaves at arbitrarily small angle. Such an object is called a virtual leaf here.