Non-separating immersions of spheres and Bing houses
type: Item
instance of: scholarly article
title: Non-separating immersions of spheres and Bing houses
zbMATH Open document ID: 1493.57024
author: Yanyan Li
published in: Mathematical Research Letters
publication date: 2021-11-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1911.08858
review text: In [Ann. Math. (2) 87, 29--41 (1968; Zbl 0159.23902)], \textit{A. D. Weinstein} stated the theorem below that allows us to deduce the existence of non-separating PL immersions of \(S^{n-1}\) into \(\mathbb R^{n}\) for \( n \geq 3\). Weinstein's Theorem: ``For any closed, smooth manifold \(M^{n}\) of dimension \(n \geq 2\) that is not the sphere \(S^{ 2}\), there is a Riemannian metric and a point \(p \in M\) whose conjugate locus is disjoint from the cut locus.'' This paper presents an explicit and fascinating construction of a \(3\)-dimensional Bing house example, discovered in 1950, but never published, which is an immersion of \(S^{2}\) into \(S^{3}\). Also for \(n \geq 4\), the authors construct explicit non-separating, locally flat, PL immersions of \(S^{n-1}\) into \(S^{n}\).
reviewed by: Alice K. M. Libardi
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 7435690
zbMATH Keywords: immersions of spheres
zbMATH Keywords: Bing houses
MaRDI profile type: Publication
arXiv ID: 1911.08858
OpenAlex ID: W3216358943
DOI: 10.4310/MRL.2021.V28.N4.A5
description: scientific article