Imbedding and Immersion of Real Projective Spaces
J. Levine · Proceedings of the American Mathematical Society · 1963
We will prove the following results on the imbeddability and immersibility of real w-dimensional projective space Pn in Euclidean space.All imbeddings and immersions are differentiable.A. If n -1 is a power of two, P" cannot be imbedded in E2n~2.B. If n>7, Pn cannot be immersed in En+2.C.1 P9 can be immersed in Elb.Since P" can be imbedded in E2"-1 for n odd (see [4]), (A) solves the imbedding problem for P" when n -1 is a power of two.The immersion problem for P9 is solved by (C), since a consideration of normal Stiefel-Whitney classes shows P9 cannot be immersed in 7£14.The immersion problem for Pn, n<9, has already been solved (see 7.1 of