An Unstable Approach to the May-Lawrence Matrix Toda bracket and the \textit{2}nd James-Hopf Invariant
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916312741052416 |
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| author | Yang, Juxin Miyauchi, Toshiyuki Mukai, Juno |
| author_facet | Yang, Juxin Miyauchi, Toshiyuki Mukai, Juno |
| contents | 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 $\ct'\inπ_{26}(S^{6})$ localized at 2 which improves the construction of $\ct'$ given by \cite{20STEM}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18014 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Unstable Approach to the May-Lawrence Matrix Toda bracket and the \textit{2}nd James-Hopf Invariant Yang, Juxin Miyauchi, Toshiyuki Mukai, Juno Algebraic Topology 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 $\ct'\inπ_{26}(S^{6})$ localized at 2 which improves the construction of $\ct'$ given by \cite{20STEM}. |
| title | An Unstable Approach to the May-Lawrence Matrix Toda bracket and the \textit{2}nd James-Hopf Invariant |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2310.18014 |