\(KO\)-theory of exceptional flag manifolds
type: Item
instance of: scholarly article
title: \(KO\)-theory of exceptional flag manifolds
zbMATH Open document ID: 1277.55002
DOI: 10.1215/21562261-2265923
author: Daisuke Kishimoto
author: Akihiro Ohsita
published in: Kyoto Journal of Mathematics
publication date: 2013-09-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kjm/1376917629
review text: Let \(G\) be a compact connected Lie group and let \(T\) be a maximal torus of \(G\). In this paper the authors calculate the real \(KO\)-theory of a flag manifold \(G/T\) for the exceptional Lie groups \(G=G_2, F_4, E_6\) using the Atiyah-Hirzebruch spectral sequence and Steenrod squaring cohomology operations. Also they point out the connection between Witt groups and the real \(KO\)-theory of homogeneous spaces such as Grassmannians and flag manifolds. All calculations are done explicitly.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55T25
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 6212905
zbMATH Keywords: real \(K\)-theory
zbMATH Keywords: exceptional Lie groups
zbMATH Keywords: flag manifolds
zbMATH Keywords: Atiyah-Hirzebruch spectral sequence
zbMATH Keywords: Witt groups
zbMATH Keywords: generalized cohomology
reviewed by: Cenap Özel
MaRDI profile type: Publication
OpenAlex ID: W2052451182
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description: scientific article; zbMATH DE number 6212905