An unstable approach to the May-Lawrence matrix Toda bracket and the 2nd James-Hopf invariant

In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool to detect the unstable phenomena. Then, we give a generalization of the classical isomorphisms between homotopy groups of (JSm,Sm) and (JS2m,⁎) localized at 2. After that we provide a gen...

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Bibliographic Details
Published in:Topology and its applications 2024-10, Vol.355, p.109026, Article 109026
Main Authors: Yang, Juxin, Miyauchi, Toshiyuki, Mukai, Juno
Format: Article
Language:English
Subjects:
Box bracket
Homotopy group
Matrix Toda bracket
Second James-Hopf invariant
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Summary:In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool to detect the unstable phenomena. Then, we give a generalization of the classical isomorphisms between homotopy groups of (JSm,Sm) and (JS2m,⁎) localized at 2. After that we provide a generalized H-formula for matrix Toda brackets. As an application, we show a new construction of κ¯′∈π26(S6) localized at 2 which improves the construction of κ¯′ given by [4].
ISSN:0166-8641
DOI:10.1016/j.topol.2024.109026