On Imbedding Differentiable Manifolds in Euclidean Space
Morris W. Hirsch · Annals of Mathematics · 1961
Assume n,k,m,q are positive integers. Let M^n denote a smooth differentiable n-manifold and R^k Euclidean k-space. (a) If M^n is open it imbeds smoothly in R^k, k=2n-1 (b) If M^n is open and parallelizable it immerses in R^n (c) Assume M^n is closed and (m-1)-connected, 12n-2m, then the complement of a point of M^n imbeds smoothly in R^q.