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Juxin Yang

Publications and source records attributed to Juxin Yang.

6 recordsLinked to original sources
arXiv2025

A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex

In this paper, we determine the 3-cell skeleton of $F$, where $F$ is the homotopy fiber of the canonical pinch map from a suspension of a simply-connected 2-cell complex onto a sphere. The main result is stated $p$-locally: for $p=2$, and for $p\geq5$ under an additional assumption. The proof is based on Selick-Wu's $\mathrm{A}^{\mathrm{min}}$-theory and the machinery of the Eilenberg-Moore spectral sequence. As an application, we compute the 2-primary component of $\pi_{18} (\Sigma^{3}\mathbb{C}P^{2})$, a homotopy group outside the metastable range.

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arXiv2024

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 $(JS^{2m},*)$ 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}.

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arXiv2024

On the extension problems for three 33-stem homotopy groups

This paper tackles the extension problems for three far-unsatble homotopy groups $π_{39}(S^{6})$, $π_{40}(S^{7})$, and $π_{41}(S^{8})$ localized at 2, the puzzles having remained unsolved for forty-five years. By a Toda bracket indexed by 1 included in $π_{39}(S^{6}_{(2)})$, which makes better use of the deuspension property of homotopy classes, we address the problems. As a corollary, through Thomeier's 8-step backward theorem of the metastable homotopy theory, together with the results of Oda, Mukai and Miyauchi, we show a table of the 33-stem homotopy groups $π_{33+n}(S^{n}_{(2)})$, ($2\leq n\leq 9$, $n\geq27$).

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arXiv2024

On rectangular Toda brackets and Oda's extension problems

This paper tackles \textit{N. Oda}'s extension problems for the homotopy groups $π_{39}(S^{6})$, $π_{40}(S^{7})$, and $π_{41}(S^{8})$ localized at 2, the issues having eluded resolution for more than four decades. We introduce a tool for the theory of determinations of unstable homotopy groups, namely, the rectangular Toda bracket, by which we are able to solve the extension problems with respect to these three homotopy groups.

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arXiv2023

On the Homotopy Groups of the Suspended Quaternionic Projective Plane and Applications

In this paper, we determined the $2,3$-components of the homotopy groups $\pi _{r+k}(\Sigma ^{k}\mathbb{H}P^{2})$ for all $ 7\leq r\leq15$ and all $\;k\geq0$, especially for the unstable ones. And we gave the applications, including the classification theorems of the 1-connected CW complexes having CW types of the suspended $\mathbb{H} P^{3}$ localized at 3 , and the decompositions of the suspended self smashes.

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