Hopf rings and unstable operations
type: Item
instance of: scholarly article
title: Hopf rings and unstable operations
zbMATH Open document ID: 0824.55008
DOI: 10.1016/0022-4049(94)90032-9
author: Takuji Kashiwabara
published in: Journal of Pure and Applied Algebra
publication date: 1994-08-07T00:00:00Z
review text: Let \({\mathcal C} {\mathcal P}\) denote the full subcategory of the homotopy category of spaces whose objects are finite products of \(\mathbb{C} P^ \infty\)s. Using algebraically defined Hopf rings introduced by \textit{D. C. Ravenel} and \textit{W. S. Wilson} [ibid. 9, 241-280 (1977; Zbl 0373.57020)] the author shows that for good cohomology theories \(E^*\) and \(F^*\) the set of unstable cohomology operations from \(F\) to \(E\) (in even degrees) can be identified with the set of natural transformations from \(F\) to \(E\) when restricted to the category \({\mathcal C} {\mathcal P}\). As an application the author gives a new proof for the existence of \(BP\)- unstable Adams operations.
Mathematics Subject Classification ID: 55S25
zbMATH DE Number: 612146
zbMATH Keywords: finite products of \(\mathbb{C} P^ \infty\)s
zbMATH Keywords: \(BP\)-unstable Adams operations
zbMATH Keywords: infinite complex projective space
zbMATH Keywords: homotopy category
zbMATH Keywords: Hopf rings
zbMATH Keywords: unstable cohomology operations
reviewed by: Rolf Kultze
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90032-9
OpenAlex ID: W2011589195
cites work: Q4067782
cites work: Q4733118
cites work: Q4010480
cites work: On the structure of spaces representing a Landweber exact cohomology theory
cites work: Generic Representations of the Finite General Linear Groups and the Steenrod Algebra: I
cites work: The Sullivan conjecture on maps from classifying spaces
cites work: THE METHODS OF ALGEBRAIC TOPOLOGY FROM THE VIEWPOINT OF COBORDISM THEORY
cites work: The Hopf ring for complex cobordism
cites work: Q3667609
description: scientific article; zbMATH DE number 612146