A note on the Hopf homomorphism of a Toda bracket and its application
type: Item
instance of: scholarly article
title: A note on the Hopf homomorphism of a Toda bracket and its application
zbMATH Open document ID: 1061.55010
author: Tomohisa Inoue
author: Juno Mukai
published in: Hiroshima Mathematical Journal
publication date: 2004-12-29T00:00:00Z
review text: This paper defines a generalized Hopf homomorphism \(H : [\Sigma K, \Sigma A] \rightarrow [\Sigma K, \Sigma(A \wedge A)]\) for a CW-complex \(A\) with a single vertex. The authors relate this homomorphism to the Toda bracket. By applying their results to suspensions of the real projective plane and the quasi-quaternionic projective plane they determine, in a roundabout way, the \(2\)-primary component \(\pi_{14}^{7}\) of the homotopy group \(\pi_{14}(S^{7})\). They also give a short proof of the existence of the unstable Adam's map.
Mathematics Subject Classification ID: 55Q25
Mathematics Subject Classification ID: 55Q40
zbMATH DE Number: 2123908
zbMATH Keywords: Toda bracket
zbMATH Keywords: Hopf homomorphism
zbMATH Keywords: unstable Adam's map
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1150997982
OpenAlex ID: W1589261912
Wikidata QID: Q128872795
DOI: 10.32917/HMJ/1150997982
description: scientific article; zbMATH DE number 2123908