 There is also an analogue in homotopy theory for Poincaré spaces, the Spivak spherical fibration, named after Michael Spivak.Given an embedding of a manifold in Euclidean space (provided by the theorem of Hassler Whitney), it has a normal bundle.The embedding is not unique, but for high dimension of the Euclidean space it is unique up to isotopy, thus the (class of the) bundle is unique, and called the "stable normal bundle".