A converse of the Jordan-Brouwer theorem
We prove that, given a smooth immersion with normal crossings, \(f: M\to N\), between an \((n-1)\)-manifold \(M\) such that \(H_ 1(M,\mathbb{Z}_ 2)=0\) if \(n>2\), and an \(n\)-manifold \(N\) with \(H_ 1(N,\mathbb{Z}_ 2)=0\), then \(f\) is an embedding if and only if the number of connected components in \(N- f(M)\) is exactly 2.
scientific article; zbMATH DE number 4216269