Construction Via Classifying Spaces
An n-manifold M has a tangent bundle, which has a classifying map (up to homotopy)
Composing with the inclusion yields (the homotopy class of a classifying map of) the stable tangent bundle. The normal bundle of an embedding ( large) is an inverse for, such that the Whitney sum 
is trivial. The homotopy class of the composite is independent of the choice of inverse, classifying the stable normal bundle .
Read more about this topic: Stable Normal Bundle
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