Equivariant connective \(K\)-theory for compact Lie groups.
type: Item
instance of: scholarly article
title: Equivariant connective \(K\)-theory for compact Lie groups.
zbMATH Open document ID: 1043.19004
published in: Journal of Pure and Applied Algebra
publication date: 2004-02-02T00:00:00Z
review text: This paper gives a construction of a \(G\)-spectrum \(ku\), for \(G\) a compact Lie group, which is a \(G\)-equivariant analog of connective \(K\)-theory. It is a complex oriented, ring valued theory from which Atiyah-Segal equivariant \(K\)-theory can be obtained by inverting the Bott class and for which completion with respect to the augmentation ideal yields non-equivariant connective \(K\)-theory. Partial results are given concerning the coefficient ring \(ku_*^G\). For non-negative degrees, these agree with those of periodic \(K\)-theory and for degrees above \(-6\) they are described in terms of \(R(G)\). It is also shown that \(ku^G_{-6}\) can contain torsion.
Mathematics Subject Classification ID: 19L41
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 19L47
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 2035897
zbMATH Keywords: equivariant K-Theory
zbMATH Keywords: compact Lie group
zbMATH Keywords: Rees ring
author: John Greenlees
reviewed by: Keith Johnson
MaRDI profile type: Publication
full work available at URL: j.jpaa.2003.07.008
OpenAlex ID: W2021493603
Wikidata QID: Q115345660
cites work: The connective 𝐾-theory of finite groups
cites work: Equivariant formal group laws
cites work: The universality of equivariant complex bordism
cites work: Q4716283
cites work: Algebras over equivariant sphere spectra
cites work: \(K\)-homology of universal spaces and local cohomology of the representation ring
cites work: Augmentation ideals of equivariant cohomology rings
cites work: Equivariant forms of connective K-theory
cites work: Multiplicative equivariant formal group laws.
cites work: From elliptic curves to homotopy theory
cites work: Equivariant stable homotopy theory. With contributions by J. E. McClure
DOI: 10.1016/J.JPAA.2003.07.008
description: scientific article; zbMATH DE number 2035897