Relations among generalized characteristic classes
type: Item
instance of: scholarly article
title: Relations among generalized characteristic classes
zbMATH Open document ID: 0727.57023
author: Alexander E. Koonce
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: In Topology 3, Suppl. 1, 39-82 (1964; Zbl 0137.427), \textit{E. H. Brown} and \textit{F. P. Peterson} determined the elements of \(H^*(BO;{\mathbb{Z}}/2)\) which vanish on the normal bundles of all n-manifolds. This paper generalizes their result by replacing BO by the classifying space B associated to a class of manifolds and by replacing \(H^*(-;{\mathbb{Z}}/2)\) by a generalized cohomology theory \(E^*\) satisfying some mild orientability conditions. The main general result reduces the determination of these classes to consideration of a stabilization map and a switch map. It is shown that this very general result reduces to Brown and Peterson's in the classical case, and an explicit calculation is made when \(B=BU\) and E is the Morava K-theory K(m).
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 4201172
zbMATH Keywords: normal bundles
zbMATH Keywords: n-manifolds
zbMATH Keywords: classifying space
zbMATH Keywords: generalized cohomology theory
zbMATH Keywords: Morava K-theory
MaRDI profile type: Publication
full work available at URL: pjm.1990.145.239
OpenAlex ID: W2038299467
DOI: 10.2140/PJM.1990.145.239
description: scientific article; zbMATH DE number 4201172