  A first order Vassiliev invariant of an oriented knot in an $S^1$-fibration
and a Seifert fibration over a surface is constructed. It takes values in a
quotient of the group ring of the first homology group of the total space of
the fibration. It gives rise to an invariant of wave fronts on surfaces and
orbifolds related to the Bennequin-type invariants of the Legendrian curves
studied by F. Aicardi, V. Arnold, M. Polyak, and S. Tabachnikov. Formulas
expressing these relations are presented.
  We also calculate Turaev's shadow for the Legendrian lifting of a wave front.
This allows to use in the case of wave fronts all invariants known for shadows.
