obstructions to the existence of such maps are often formulated algebraically from the topological data of formula_3 and formula_46. an archetypal example of such an obstruction can be derived having formula_42 a vector space and formula_48. in this case, a nonvanishing map would also induce a nonvanishing section formula_49 from the discussion above, so formula_50, the top stiefel–whitney class would need to vanish.