\(J\)-groups of the quaternionic spherical space forms
type: Item
instance of: scholarly article
title: \(J\)-groups of the quaternionic spherical space forms
zbMATH Open document ID: 0824.55005
published in: Hiroshima Mathematical Journal
publication date: 1994-11-03T00:00:00Z
review text: Let \(Q_ m\) \((m \geq 2)\) be the subgroup of the unit sphere \(S^ 3\) in the quaternion field \(H\) generated by the two elements \(x = \exp (\pi i/2^{m - 1})\) and \(y = j\). The action of \(Q_ m\) on the unit sphere \(S^{4n + 3}\) in the quaternion \((n + 1)\)-space is given by the diagonal action. Let \(N^ n (m)\) denote the quotient manifold \(S^{4n + 3}/Q_ m\). Using the orthogonal representation ring \(RO (Q_ m)\) and the additive structure of \(\widetilde {KO} (N^ n (m))\) the author determines the structure of the reduced \(J\)-group \(\widetilde J(N^ n (m))\) for all \(m \geq 2\).
Mathematics Subject Classification ID: 55Q50
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 681279
zbMATH Keywords: unit sphere in the quaternion field
zbMATH Keywords: quaternion \((n + 1)\)-space
zbMATH Keywords: \(J\)- group
zbMATH Keywords: real \(K\)-theory
zbMATH Keywords: representation ring
author: Kenso Fujii
reviewed by: Rolf Kultze
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206128031
OpenAlex ID: W1575462916
DOI: 10.32917/HMJ/1206128031
description: scientific article; zbMATH DE number 681279