\(KO\)-rings of \(S^{2k+1}/\mathbb{Z} z_{2^n}\)
type: Item
instance of: scholarly article
title: \(KO\)-rings of \(S^{2k+1}/\mathbb{Z} z_{2^n}\)
zbMATH Open document ID: 0892.55006
DOI: 10.1023/A:1007705425792
author: Mehmet Kirdar
published in: \(K\)-Theory
publication date: 1998-07-21T00:00:00Z
review text: Let \(L_k(2^n)\) be the quotient \(S^{2k+1}/Z_{2^n}\), where the group \(Z_{2^n}\) of complex \(2^n\)th roots of unity acts on unit sphere \(S^{2k+1}\) in \(C^{k+1}\) in the usual way: \(z(z_0, \dots, z_k) =(zz_0, \dots, zz_k)\). In this note the author gives generators and relations for the real \(K\)-group \(KO(L_k (2^n))\), \(n\geq 2\). Using this result the author also determines the orders of powers of the element in \(KO(L_k (2^n))\) which arises from the canonical complex line bundle over \(L_k(2^n)\).
reviewed by: Haruo Minami
Mathematics Subject Classification ID: 55R50
Mathematics Subject Classification ID: 55Q50
zbMATH DE Number: 1132935
zbMATH Keywords: lens spaces
zbMATH Keywords: stable classes of vector bundles
zbMATH Keywords: Atiyah-Hirzebruch spectral sequence
MaRDI profile type: Publication
full work available at URL: a:1007705425792
OpenAlex ID: W2335328461
description: scientific article; zbMATH DE number 1132935