KO-theory of complex Grassmannians
type: Item
instance of: scholarly article
title: KO-theory of complex Grassmannians
zbMATH Open document ID: 0748.57015
author: Akira Kono
author: Shin-ichiro Hara
published in: Journal of Mathematics of Kyoto University
publication date: 1992-09-27T00:00:00Z
review text: Let \(M_{m,n}\) be the complex Grassmann manifold \(G_ m(C^{m+n})\) of \(m\)-planes in \(C^{m+n}\). There is a homeomorphism: \(M_{m,n}\buildrel\simeq\over \longrightarrow U(m+n)/U(m)\times U(n)\). The \(KO^ i\)-groups of \(M_{m,n}\) are studied by \textit{S. G. Hoggar} [Q. J. Math., Oxf. II. Ser. 20, 447-463 (1969; Zbl 0184.484)]. The free parts of them are determined, but the torsion parts are partially known [\textit{Hoggar}, loc. cit.; \textit{S. A. Ilori}, K-Theory 2, No. 5, 623-624 (1989; Zbl 0671.55005)]. Here we compute them for arbitrary \(m\) and \(n\), using only the Atiyah-Hirzebruch spectral sequence.
Mathematics Subject Classification ID: 57T15
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55T25
zbMATH DE Number: 59745
zbMATH Keywords: complex Grassmann manifold
zbMATH Keywords: \(KO^ i\)-groups
zbMATH Keywords: Atiyah-Hirzebruch spectral sequence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519732
OpenAlex ID: W1483693083
DOI: 10.1215/KJM/1250519732
description: scientific article; zbMATH DE number 59745