Characteristic Cycles of Manifolds

Let R ^k+l be (k + l)-dimensional Euclidean space, and H(k, l) the manifold of all oriented k-dimensional planes in the space R ^k+l that pass through a fixed point O. Let M be a k-dimensional oriented manifold with a continuous tangent in R ^k+l . To each point x of the manifold M^k let us put into correspondence that plane T(x) in H(k, l) which is parallel to the tangent to the manifold M at the point x. Evidently, under a continuous differentiable deformation of M^k in R^k+l , the mapping T changes continuously, and consequently, the homotopy type of this mapping remains invariant.