Polynomial operations on stable cohomotopy
type: Item
instance of: scholarly article
title: Polynomial operations on stable cohomotopy
zbMATH Open document ID: 0708.55016
DOI: 10.1007/BF02568437
author: Ernesto Vallejo
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155504
review text: Following ideas of G. Segal, the author gives a conceptual framework for the study of a wide class of unstable operations from the 0th stable cohomotopy group \(\pi^ 0_ s\) to other homotopy functors. These include symmetric powers especially. The concept of polynomial operations is defined and one gets a ring \(Pol(\pi^ 0_ s,\pi^ 0_ s)\). This ring is isomorphic to \(Pol(A,\hat A)\) where A is the Burnside ring and \(\hat A\) is the completed Burnside functor using augmentation ideals. Here the Pol denotes the ring of polynonial maps. This isomorphism is the paper's main result. The paper mentions characteristic classes, K-theory, and transfers of finite coverings.
Mathematics Subject Classification ID: 55S99
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 4163739
zbMATH Keywords: unstable operations
zbMATH Keywords: stable cohomotopy group
zbMATH Keywords: symmetric powers
zbMATH Keywords: polynomial operations
zbMATH Keywords: Burnside ring
zbMATH Keywords: characteristic classes
zbMATH Keywords: K-theory
zbMATH Keywords: transfers
zbMATH Keywords: finite coverings
reviewed by: Daniel H. Gottlieb
MaRDI profile type: Publication
cites work: Infinite Loop Spaces (AM-90)
cites work: Characters and cohomology of finite groups
cites work: Equivariant stable homotopy and Segal's Burnside ring conjecture
cites work: James Maps, Segal Maps, and the Kahn-Priddy Theorem
cites work: Q4724810
cites work: K-theory of non-additive functors of finite degree
cites work: Q3681565
cites work: The Burnside ring of profinite groups and the Witt vector construction
cites work: The Burnside ring of the infinite cyclic group and its relations to the necklace algebra, \(\lambda\)-rings, and the universal ring of Witt vectors
cites work: On the groups \(H(\Pi,n)\). II
cites work: Axiomatic representation threory for finite groups
cites work: Q3914088
cites work: On the Burnside ring and stable cohomotopy of a finite group.
cites work: Q4766246
cites work: Q3687345
cites work: Construction of universal bundles. II
cites work: Characteristic Classes. (AM-76)
cites work: Polynomial maps on groups
cites work: Categories and cohomology theories
cites work: Q5182860
cites work: Characteristic classes for permutation representations
cites work: Polynomial operations from Burnside rings to representation functors
OpenAlex ID: W2040432070
description: scientific article; zbMATH DE number 4163739