On the Koschorke normal bordism sequence
type: Item
instance of: scholarly article
title: On the Koschorke normal bordism sequence
zbMATH Open document ID: 0786.57014
published in: Science in China. Series A
publication date: 1993-05-16T00:00:00Z
review text: This paper considers the normal bordism group \(\Omega_ n(X,\varphi)\), \(\varphi\in K\widetilde{O}(X)\), consisting of bordism classes of pairs \((g,G)\), with \(g: M\to X\), \(M\) a closed \(n\)-manifold and \(G\) a trivialization of \(\tau M\oplus g^*\varphi\) (\(\tau M\) the tangent bundle of \(M\)). These groups appear, for example, in the work of Koschorke on the vector field problem and in the classification of immersions. The results in the present paper describe explicit relations between \(\Omega_ n(X,\varphi)\) and \(H_ n(X,Z_ \varphi)\) for \(n=1\) and 2, where \(Z_ \varphi\) is the twisted \(Z\) defined by \(w_ 1(\varphi)\). The precise relations depend on various technical conditions. There are also results on \(\Omega_ n(X\times \text{BO}(2),\varphi\times \Gamma)\), where \(\Gamma\) is the universal bundle (also for \(n=1\) and 2).
Mathematics Subject Classification ID: 57R90
zbMATH DE Number: 167262
zbMATH Keywords: first Stiefel-Whitney class
zbMATH Keywords: orientation bundle
zbMATH Keywords: normal bordism
zbMATH Keywords: universal bundle
author: Bang-He Li
reviewed by: Jerome Levine
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 167262