On codimension-1 submanifolds of the real and complex projective space

Abstract

Inspired by the analogous result in the algebraic setting (Theorem 1) we show (Theorem 2) that the product $M\times \mathbb{R}{P}^n$ of a closed and orientable topological manifold $M$ with the $n$-dimensional real projective space cannot be topologically locally flat embedded into $\mathbb{R}{P}^{m+n+1}$ for all even $n>m$.

To appear in Topology and its Applications