T. Miyauchi

activity

20072026

most citedOn Lusternik-Schnirelmann category of SO(10)

5 citations · 10 across the 8 of their papers we have counts for

collaborators

9 papers

math.AT2026

Relations in the 24-th homotopy groups of spheres

Toshiyuki Miyauchi, Juno Mukai

The main purpose of this note is to give a proof of the fact that the Toda brackets \ $⟨ ν ˉ, σ, ν ˉ ⟩$ and $⟨ ν, η, σ ˉ ⟩$ are not trivial. This is an affir…

math.AT2023

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

Juxin Yang, Toshiyuki Miyauchi, Juno Mukai

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,…

math.AT2023

Homotopy commutativity in symmetric spaces

Daisuke Kishimoto, Yuki Minowa, Toshiyuki Miyauchi +1

We extend the former results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric spaces such that the loop space…

math.AT2021

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

Yoshihiro Hirato, Jin-ho Lee, Toshiyuki Miyauchi +2

We denote by $π_{k} (R_{n})$ the $k$ -th homotopy group of the $n$ -th rotation group $R_{n}$ and $π_{k} (R_{n} : 2)$ the 2-primary components of it. We determine the group structures of $π_k(R_n:…

math.AT2019★ 1 cited

Higher homotopy associativity in the Harris decomposition of Lie groups

Daisuke Kishimoto, Toshiyuki Miyauchi

Let $(G, H) = (S U (2 n + 1), S O (2 n + 1)), (S U (2 n), S p (n)), (S O (2 n), S O (2 n - 1)), (E_{6}, F_{4}), (S p in (8), G_{2})$ , and let $p$ be any prime $\geq 5$ for $(G, H) = (E_{6}, F_{4})$ , any prime $p \neq = 3$ for $(G…

math.AT2017

On Mimura's extension problem

Toshiyuki Miyauchi, Juno Mukai, Mariko Ohara

We determine the group strucure of the $23$ -rd homotopy group $π_{23} (G_{2} : 2)$ , where $G_{2}$ is the Lie group of exceptional type, which hasn't been determined for $50$ years.

math.AT2017★ 2 cited

Samelson products in quasi- $p$ -regular exceptional Lie groups

Sho Hasui, Daisuke Kishimoto, Toshiyuki Miyauchi +1

There is a product decomposition of a compact connected Lie group $G$ at the prime $p$ , called the mod $p$ decomposition, when $G$ has no $p$ -torsion in homology. Then in studying…

math.AT2012★ 2 cited

Relations in the 24-th homotopy groups of spheres

Toshiyuki Miyauchi, Juno Mukai

The main purpose of this note is to give a proof of the fact that the Toda brackets $< ν ˉ, σ, ν ˉ >$ and $< ν, η, σ ˉ >$ are not trivial. This is an affirmative answer of the secon…

math.AT2007★ 5 cited

On Lusternik-Schnirelmann category of SO(10)

Norio Iwase, Kai Kikuchi, Toshiyuki Miyauchi

Let $G$ be a compact connected Lie group and $p : E \to Σ A$ be a principal G-bundle with a characteristic map $α : A \to G$ , where $A = Σ A_{0}$ for some $A_{0}$ . Let $\{K_{i}{\to} F_{i-…

Relations in the 24-th homotopy groups of spheres

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

Homotopy commutativity in symmetric spaces

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

Higher homotopy associativity in the Harris decomposition of Lie groups

On Mimura's extension problem

Samelson products in quasi-p-regular exceptional Lie groups

Relations in the 24-th homotopy groups of spheres

On Lusternik-Schnirelmann category of SO(10)

Samelson products in quasi- $p$ -regular exceptional Lie groups