Masahiro Takeda

activity

20192022

collaborators

4 papers

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.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

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…

Homotopy commutativity in Hermitian symmetric spaces

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

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