On bordism invariance of an obstruction to topological embeddings
type: Item
instance of: scholarly article
title: On bordism invariance of an obstruction to topological embeddings
zbMATH Open document ID: 0883.57030
author: Carlos Biasi
author: Osamu Saeki
published in: Osaka Journal of Mathematics
publication date: 1998-03-09T00:00:00Z
review text: In previous papers, the authors have defined an obstruction class \(\theta(f)\) for a map \(f:M \to N\) between smooth manifolds with \(k=\dim N- \dim M>0\) to be homotopic to an embedding. The class is defined using Stiefel-Whitney classes and Gysin homomorphisms. Here they consider two maps \(f,g:M\to N\) which are bordant and ask whether \(\theta(f)= \theta(g)\). This is shown to be true if \(H^{m-k} (M;Z_2)\) \((m= \dim M)\) consists entirely of characteristic classes. This unpleasant condition is used to force \(f^*=g^*\) on \(k\)-dimensional cohomology and is not really what one wishes.
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 55S35
zbMATH DE Number: 1018462
zbMATH Keywords: Stiefel-Whitney classes
zbMATH Keywords: Gysin homomorphisms
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1018462