The 23-rd and 24-th homotopy groups of the n-th rotation group

We denote by $\pi_k(R_n)$ the $k$-th homotopy group of the $n$-th rotation group $R_n$ and $\pi_k(R_n:2)$ the 2-primary components of it. We determine the group structures of $\pi_k(R_n:2)$ for $k = 23$ and $24$ by use of the fibration $R_{n+1}\overset{R_n}{\longrightarrow}S^n$. The method is based...

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Bibliographic Details
Main Authors Hirato, Yoshihiro, Lee, Jin-ho, Miyauchi, Toshiyuki, Mukai, Juno, Ohara, Mariko
Format Journal Article
LanguageEnglish
Published 30.06.2021
Subjects
Mathematics - Algebraic Topology
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Summary:We denote by $\pi_k(R_n)$ the $k$-th homotopy group of the $n$-th rotation group $R_n$ and $\pi_k(R_n:2)$ the 2-primary components of it. We determine the group structures of $\pi_k(R_n:2)$ for $k = 23$ and $24$ by use of the fibration $R_{n+1}\overset{R_n}{\longrightarrow}S^n$. The method is based on Toda's composition methods.
DOI:10.48550/arxiv.2107.00154