The order of the attaching class in the suspended quaternionic quasi- projective space
type: Item
instance of: scholarly article
title: The order of the attaching class in the suspended quaternionic quasi- projective space
zbMATH Open document ID: 0562.55014
author: Juno Mukai
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: Let \(Q_ n(H)\) denote the quaternionic quasi-projective n-space. Then \(Q_ n(H)\) is formed from \(Q_{n-1}(H)\) by attaching the cell \(e^{4n- 1}\) via a map \(T_ n\). In this paper the author determines the order \(o_{n,k}\) of the homotopy class of the suspension \(E^ kT_ n\) as follows: if n is even then \(o_{n,k}=2\cdot (2n-1)!\) and, if n is odd then \(o_{n,\infty}=(2n-1)!\). The proof proceeds by using the results of \textit{M. Mimura} and \textit{H. Toda} [J. Math. Kyoto Univ. 3, 251-273 (1964; Zbl 0129.154)] on \(\pi_{4n-2}(Sp(n-1))\) and by invoking the K- theoretic consideration in order to evaluate the lower bound of \(o_{n,k}\).
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 57T20
zbMATH DE Number: 3895944
zbMATH Keywords: symplectic groups
zbMATH Keywords: stunted quasi-projective spaces
zbMATH Keywords: homotopy groups
zbMATH Keywords: quaternionic quasi-projective n-space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195181109
OpenAlex ID: W2012219682
cites work: The homotopy groups of a triad. II
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DOI: 10.2977/PRIMS/1195181109
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description: scientific article; zbMATH DE number 3895944