Editing Whitney embedding theorem (section)

===Eventual consequences of the Whitney trick===
The Whitney trick was used by [[Stephen Smale]] to prove the [[h-cobordism theorem|''h''-cobordism theorem]]; from which follows the [[Poincaré conjecture]] in dimensions {{math|''m'' ≥ 5}}, and the classification of [[smooth structure]]s on discs (also in dimensions 5 and up). This provides the foundation for [[surgery theory]], which classifies manifolds in dimension 5 and above.

Given two oriented submanifolds of complementary dimensions in a simply connected manifold of dimension ≥ 5, one can apply an isotopy to one of the submanifolds so that all the points of intersection have the same sign.