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 × RP n of a closed and orientable topological manifold M with the n-dimensional real projective space cannot be topologically locally flat embedded into RP m+n+1 for all even n > m.2010 Mathematics Subject Classification. 32H02, 57N35.