The quasi \(KO_*\)-types of CW-spectra \(X\) with \(KU_0 X\cong Z/2^m\) and\(KU_1X\cong Z/2^n\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0971.55005
author: Zen-ichi Yosimura
publication date: 2001-08-14T00:00:00Z
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 1605048
zbMATH Keywords: stable homotopy theory
zbMATH Keywords: quasi KO-type
MaRDI profile type: Publication
title: The quasi \(KO_*\)-types of CW-spectra \(X\) with \(KU_0 X\cong Z/2^m\) and\(KU_1X\cong Z/2^n\)
published in: Memoirs of the Faculty of Science. Series A. Mathematics
review text: Two CW spectra \(X, Y\) are said to be quasi \(KO_*\)-equivalent if \(KO \wedge X\) and \(KO \wedge Y\) are isomorphic as \(KO\)-module spectra. In earlier papers the author has described the possible quasi \(KO_*\)-types of spectra with \(KU_* X\) free or of the form \(\text{free }\oplus {\mathbb Z}/2^m {\mathbb Z}\) [Osaka J. Math 27, No. 3, 465-498 (1990; Zbl 0719.55007); 36, No. 4, 747-765 (1999; Zbl 0953.55008)]. These questions have also been studied by \textit{A. K. Bousfield} [J. Pure Appl. Algebra 66, No. 2, 121-163 (1990; Zbl 0713.55007)]. The present paper extends this description to the case in which \(KU_* X\) is as described in the title. The method is to construct small spectra of the required sort, calculate their \(KC\)-homology and involution and then show these enumerate all possible quasi \(KO_*\)-types. The list of types is too long to give here.
reviewed by: Keith Johnson
description: scientific article; zbMATH DE number 1605048