 More abstractly, rather than stabilizing the embedding, one can take any embedding, and then take a vector bundle direct sum with a sufficient number of trivial line bundles; this corresponds exactly to the normal bundle of the stabilized embedding.An "n"-manifold "M" has a tangent bundle, which has a classifying map (up to homotopy)

Composing with the inclusion formula_14 yields (the homotopy class of a classifying map of) the stable tangent bundle.The normal bundle of an embedding formula_15 (formula_16 large) is an inverse formula_17 for formula_18, such that the Whitney sum formula_19 is trivial.