  We study the geodesic flow of a compact surface without conjugate points and
genus greater than one and continuous Green bundles. Identifying each strip of
bi-asymptotic geodesics induces an equivalence relation on the unit tangent
bundle. Its quotient space is shown to carry the structure of a 3-dimensional
compact manifold. This manifold carries a canonically defined continuous flow
which is expansive, time-preserving semi-conjugate to the geodesic flow, and
has a local product structure. An essential step towards the proof of these
properties is to study regularity properties of the horospherical foliations
and to show that they are indeed tangent to the Green subbundles. As an
application it is shown that the geodesic flow has a unique measure of maximal
entropy.
