An Unstable Approach to the May-Lawrence Matrix Toda bracket and the \textit{2}nd James-Hopf Invariant

In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool for the theory of determinations of unstable homotopy groups. Then, we give a generalization of the classical isomorphisms between homotopy groups of \((JS^{m},S^{m}) \) and \((JS^{2m},*)...

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Bibliographic Details
Published inarXiv.org
Main Authors Yang, Juxin, Miyauchi, Toshiyuki, Mukai, Juno
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.07.2024
Subjects
Brackets
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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 for the theory of determinations of unstable homotopy groups. Then, we give a generalization of the classical isomorphisms between homotopy groups of \((JS^{m},S^{m}) \) and \((JS^{2m},*)\) localized at 2. After that we provide a generalized \(H\)-formula for matrix Toda brackets. As an application, we show a new construction of \(\ct'\in\pi_{26}(S^{6})\) localized at 2 which improves the construction of \(\ct'\) given by \cite{20STEM}.
ISSN:2331-8422