Higher cohomology operations, exotic characteristic classes and spherical fibrations
type: Item
instance of: scholarly article
title: Higher cohomology operations, exotic characteristic classes and spherical fibrations
zbMATH Open document ID: 0862.55014
author: Neeta Singh
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1996-04-28T00:00:00Z
review text: Let \(BSG\) be the classifying space for spherical fibrations. Let \(p\) be an odd prime and let all cohomology have coefficients in \(\mathbb{Z}/p\). We have \(j:BSO \to BSG\) and the \(J\)-homomorphism \(J_*: \pi_* (BSO) \to \pi_*(BSG)\). Tsuchiya computed \(H^*(BSG) \cong P(q_i) \otimes E(\beta q_i) \otimes C\), where the \(q_i\) are Wu classes. Sullivan gave a \(p\)-local splitting \(BSG_{(p)} \simeq BJ_p \times B \text{Coker} J_p\). The author proves a conjecture of Peterson that \(H^* (\text{Coker} J_p) \cong C\) as algebras over the mod \(p\) Steenrod algebra. Cohomology classes of \(H^* (BSG)\) which lie in the kernel of \(j^*\) and which are not generated by Wu classes are the exotic (primary) characteristic classes. The author gives a criterion for proving the nontriviality of higher order exotic characteristic classes.
Mathematics Subject Classification ID: 55S20
Mathematics Subject Classification ID: 55R25
zbMATH DE Number: 871000
zbMATH Keywords: \(J\)-homomorphism
zbMATH Keywords: cohomology
zbMATH Keywords: classifying space
zbMATH Keywords: spherical fibrations
zbMATH Keywords: Wu classes
zbMATH Keywords: Steenrod algebra
reviewed by: David C. Johnson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 871000