Cobordism groups of immersions of oriented manifolds
type: Item
instance of: scholarly article
title: Cobordism groups of immersions of oriented manifolds
zbMATH Open document ID: 0797.57014
DOI: 10.1007/BF01874122
author: A. Szücs
published in: Acta Mathematica Hungarica
publication date: 1994-10-25T00:00:00Z
review text: This paper is a calculation of the cobordism group of immersions of oriented manifolds in Euclidean spaces. The approach taken is to compose the immersion with the projection of Euclidean space on a hyperplane. This idea was used by T. Banchoff and U. Koschorke who study the immersion by analyzing the singular set of the composition. The new feature here is to construct a classifying space for the cobordism of these singular maps. Using a filtration of the classifying space with simple quotient spaces, Koschorke's exact sequences arise as the homotopy exact sequences for pairs. Here the spectral sequence of the filtration is used to get results in a wider range.
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 57R90
Mathematics Subject Classification ID: 55T99
zbMATH DE Number: 556327
zbMATH Keywords: cobordism group of immersions of oriented manifolds in Euclidean spaces
zbMATH Keywords: classifying space
zbMATH Keywords: singular maps
zbMATH Keywords: spectral sequence
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01874122
OpenAlex ID: W2155683010
description: scientific article; zbMATH DE number 556327