  Let U be a unipotent group over the field of complex numbers C, acting on a
complex algebraic variety X. Assume that there exists a surjective morphism of
complex algebraic varieties f: X --> Y whose fibres are orbits of U. We show
that if X and Y are smooth and all orbits of U in X have the same dimension,
then the induced map on C-points X(C) --> Y(C) is a homotopy equivalence.
Moreover, if U, X, Y, and f are defined over the field of real numbers R, then
the induced map on R-points X(R) --> Y(R) is surjective and induces homotopy
equivalences on connected components.
