Masahiro Takeda

activity

20192023

most citedTverberg's theorem for cell complexes

2 citations · 5 across the 9 of their papers we have counts for

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9 papers · 1 filter

math.AT2023

The space of commuting elements in a Lie group and maps between classifying spaces

Daisuke Kishimoto, Masahiro Takeda, Mitsunobu Tsutaya

Let $π$ be a discrete group, and let $G$ be a compact connected Lie group. Then there is a map $Θ : Hom (π, G)_{0} \to map_{*} (B π, B G)_{0}$ between the null-components of…

math.AT2022

Homotopy commutativity in Hermitian symmetric spaces

Daisuke Kishimoto, Masahiro Takeda, Yichen Tong

Ganea proved that the loop space of $C P^{n}$ is homotopy commutative if and only if $n = 3$ . We generalize this result to that the loop spaces of all irreducible Hermitian sym…

math.AT2021

Homotopy types of gauge groups over Riemann surfaces

Masaki Kameko, Daisuke Kishimoto, Masahiro Takeda

Let $G$ be a compact connected Lie group with $π_{1} (G) ≅ Z$ . We study the homotopy types of gauge groups of principal $G$ -bundles over Riemann surfaces. This can be appli…

math.AT2021★ 1 cited

Torsion in the space of commuting elements in a Lie group

Daisuke Kishimoto, Masahiro Takeda

Let $G$ be a compact connected Lie group, and let $Hom (Z^{m}, G)$ be the space of pairwise commuting $m$ -tuples in $G$ . We study the problem of which primes $p$ $\ma…

math.AT2021★ 2 cited

Tverberg's theorem for cell complexes

Sho Hasui, Daisuke Kishimoto, Masahiro Takeda +1

The topological Tverberg theorem states that any continuous map of a $(d + 1) (r - 1)$ -simplex into the Euclidean $d$ -space maps some points from $r$ pairwise disjoint faces of the simp…

math.AT2020

Cohomology of the spaces of commuting elements in Lie groups of rank two

Masahiro Takeda

Let $G$ be the classical group, and let Hom $(Z^{m}, G)$ denote the space of commuting $m$ -tuples in $G$ . Baird proved that the cohomology of Hom $(Z^{m}, G)$ is identifi…

math.AT2020★ 1 cited

Note on Samelson products in exceptional Lie groups

Daisuke Kishimoto, Akihiro Ohsita, Masahiro Takeda

We determine (non-)triviality of Samelson products of inclusions of factors of the mod $p$ decomposition of $G_{(p)}$ for $(G, p) = (E_{7}, 5), (E_{7}, 7), (E_{8}, 7)$ . This completes the determ…

math.AT2020

Spaces of commuting elements in the classical groups

Daisuke Kishimoto, Masahiro Takeda

Let $G$ be the classical group, and let Hom $(Z^{m}, G)$ denote the space of commuting $m$ -tuples in $G$ . First, we refine the formula for the Poincaré series of Hom$(\mathbb{…

math.AT2019

Cohomology of the classifying spaces of $U (n)$ -gauge groups over the 2-sphere

Masahiro Takeda

A gauge group is the topological group of automorphisms of a principal bundle. We compute the integral cohomology ring of the classifying spaces of gauge groups of principal U(n)-b…

The space of commuting elements in a Lie group and maps between classifying spaces

Homotopy commutativity in Hermitian symmetric spaces

Homotopy types of gauge groups over Riemann surfaces

Torsion in the space of commuting elements in a Lie group

Tverberg's theorem for cell complexes

Cohomology of the spaces of commuting elements in Lie groups of rank two

Note on Samelson products in exceptional Lie groups

Spaces of commuting elements in the classical groups

Cohomology of the classifying spaces of U(n)-gauge groups over the 2-sphere

Cohomology of the classifying spaces of $U (n)$ -gauge groups over the 2-sphere