A converse of the Jordan-Brouwer theorem
type: Item
instance of: scholarly article
title: A converse of the Jordan-Brouwer theorem
zbMATH Open document ID: 0739.57020
author: Carlos Biasi
author: Carmen Romero-Fuster
published in: Illinois Journal of Mathematics
publication date: 1992-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 55M05
zbMATH DE Number: 4216269
zbMATH Keywords: connected components of the complement
zbMATH Keywords: smooth immersion with normal crossings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4216269