Knotted Klein bottles with only double points
type: Item
instance of: scholarly article
title: Knotted Klein bottles with only double points
zbMATH Open document ID: 1035.57013
author: Akiko Shima
published in: Osaka Journal of Mathematics
publication date: 2003-10-27T00:00:00Z
review text: The author considers a Klein bottle \(F\) embedded in \({\mathbb R}^4\) such that the singular set of the projection from \({\mathbb R}^4={\mathbb R}^3\times{\mathbb R}\) to \({\mathbb R}^3\times\{0\}\), restricted to \(F\), consists only of double points. The main result is that \(F\) is either a ribbon Klein bottle or is obtained from a spun Klein bottle by \(m\)-fusion. (These concepts are defined in the paper.) It is also shown that if every component of the singular set on \(F\) is not null-homotopic, and \(\pi_1\left({\mathbb R}^4\setminus F\right)\cong{\mathbb Z}_2\), then \(F\) bounds a solid Klein bottle in \({\mathbb R}^4\).
Mathematics Subject Classification ID: 57Q35
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 1997257
zbMATH Keywords: knotted Klein bottle
zbMATH Keywords: ribbon Klein bottle
zbMATH Keywords: spun Klein bottle
reviewed by: C. Kearton
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1997257