A transfer map for singular fibrations
type: Item
instance of: scholarly article
title: A transfer map for singular fibrations
zbMATH Open document ID: 0687.55006
DOI: 10.1007/BF02765888
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: In this interesting paper the author constructs a transfer map on the chain level for fibrations with singularities. These give a chain construction for Oliver's transfer as well as for fibrations. This transfer is natural with respect to composition of fibre maps and with decomposition of the total space. The singular fibrations for which this transfer is defined are PL maps f: \(E\to B\) so that f is a fibration away from a codimension 2 subcomplex of B. To construct the chain map the author ``blows up'' the usual singular chain complex to a much bigger group of things he calls compact singular chains. These are formed from maps of the type \(\Delta_ q\times L\to X.\) The construction of the transfer is related to the chain level representation of the transfer of Munkholm's. In fact, in some sense he shows here how to use Munkholm's chain level transfer to enhance Larry Smith's transfer construction from discrete to non-discrete fibres.
reviewed by: Daniel H. Gottlieb
Mathematics Subject Classification ID: 55R15
zbMATH DE Number: 4126306
zbMATH Keywords: Oliver's transfer
zbMATH Keywords: PL maps
zbMATH Keywords: singular chain complex
author: Emmanuel D. Farjoun
MaRDI profile type: Publication
cites work: Q5813687
cites work: Higher simple homotopy theory
cites work: The equivariant triangulation theorem for actions of compact Lie groups
cites work: Equivariant homotopy and cohomology theory
cites work: A chain level transfer homomorphism for PL fibrations
cites work: Transfer and ramified coverings
cites work: Triangulation of stratified fibre bundles
cites work: Q3977618
full work available at URL: https://doi.org/10.1007/bf02765888
OpenAlex ID: W2147307017
description: scientific article; zbMATH DE number 4126306