Editing Homotopy group (section)

===== Application to sphere bundles =====
Milnor<ref>{{cite journal|last=Milnor|first=John|date=1956|title=On manifolds homeomorphic to the 7-sphere|journal=Annals of Mathematics|volume=64|issue=2 |pages=399–405|doi=10.2307/1969983 |jstor=1969983 }}</ref> used the fact <math>\pi_3(\mathrm{SO}(4)) = \Z\oplus\Z</math> to classify 3-sphere bundles over <math>S^4,</math> in particular, he was able to find [[exotic sphere]]s which are [[smooth manifold]]s called [[Milnor's sphere|Milnor's spheres]] only homeomorphic to <math>S^7,</math> not [[diffeomorphic]]. Note that any sphere bundle can be constructed from a <math>4</math>-[[vector bundle]], which have structure group <math>\mathrm{SO}(4)</math> since <math>S^3</math> can have the structure of an [[Oriented manifold|oriented]] [[Riemannian manifold]].