On punctured 3-manifolds in 5-sphere
type: Item
instance of: scholarly article
title: On punctured 3-manifolds in 5-sphere
zbMATH Open document ID: 0931.57023
author: Osamu Saeki
published in: Hiroshima Mathematical Journal
publication date: 2000-02-28T00:00:00Z
review text: Let \(M\) be a closed connected orientable smooth 3-manifold and \(H_1(M,\mathbb{Z})\) without torsion. Let \(M^0\) denote the punctured manifold \(M\smallsetminus \text{Int }D^3\). Then \(M\) can be embedded in the 5-sphere \(S^5\) [\textit{M. Hirsch}, Ann. Math., II. Ser. 74, 494-497 (1961; Zbl 0102.38604)]. The present paper contains the classification of embeddings of \(M^0\) in \(S^5\) up to isotopy. The classification is by the Euler class of the normal bundle of the embedding and a certain kind of Seifert linking form associated to the embedding. Similar results are proved in higher dimensions. In this case \(M\) is assumed to be a smooth closed \((n - 2)\)-connected manifold of dimension \(2n-1\), \((n\geq 3)\), which is stably parallelizable and has \(n\)-th homology group \(H_n(M,\mathbb{Z})\) without torsion. The embeddings of the punctured manifolds \(M^0\) in \(S^{2n+1}\) are classified up to almost isotopy.
reviewed by: K. H. Mayer
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 1347345
zbMATH Keywords: highly connected manifolds
zbMATH Keywords: classification of embeddings
zbMATH Keywords: punctured manifolds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1347345