  We discuss the relationship between the m-th homotopy group of the one-point
union of r copies of the two-dimensional sphere and the m-th homotopy group of
the one-point union of r+1 copies of the Thom space of the oriented
two-dimensional universal vector bundle. Using a suitably choosen isomorphism
between them a forgetful homomorphism is computed by evaluating on factors of
the Hilton splitting.
