Equivariant \(K\)-theory and maps between representation spheres
type: Item
instance of: scholarly article
title: Equivariant \(K\)-theory and maps between representation spheres
zbMATH Open document ID: 0852.55007
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1996-05-14T00:00:00Z
review text: Let \(G\) be a compact Lie group, let \(U\), \(W\) be unitary representations of \(G\), and let \(SU\) and \(SW\) be their unit spheres. The author computes their equivariant \(K\)-rings. If \(G\) is abelian and there exists a \(G\)-map \(SU \to SW\), then the author shows that \(\lambda_{-1} W \in (\lambda_{-1} U)\) in \(R(G)\) where \(\lambda_{-1} W\) is the Euler class of \(W\) in \(K_G(pt) = R(G)\) and \((\lambda_{-1} U)\) is the ideal generated by the Euler class \(\lambda_1 U\).
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 878498
zbMATH Keywords: equivariant \(K\)-theory
zbMATH Keywords: compact Lie group
zbMATH Keywords: unitary representations
zbMATH Keywords: unit spheres
zbMATH Keywords: equivariant \(K\)-rings
zbMATH Keywords: Euler class
author: Katsuhiro Komiya
reviewed by: C. S. Hoo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195163923
OpenAlex ID: W1985210872
DOI: 10.2977/PRIMS/1195163923
description: scientific article; zbMATH DE number 878498