A transfer map for singular fibrations
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.
scientific article; zbMATH DE number 4126306