Mitsunobu Tsutaya

activity

20112025

A_{n}

-equivalence types of gauge groups

7 citations · 39 across the 19 of their papers we have counts for

collaborators

21 papers

math.AT2025

Uniform Lefschetz fixed-point theory

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

We develop a Lefschetz fixed-point theory for uniformly continuous self-maps of noncompact manifolds of bounded geometry. For a uniform, simply-connected, complete Riemannian manif…

math.GT2024

Morse inequalities for noncompact manifolds

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

We establish Morse inequalities for a noncompact manifold with a cocompact and properly discontinuous action of a discrete group, where Morse functions are not necessarily invarian…

math.AT2024

Homotopy commutativity in quasitoric manifolds

Sho Hasui, Daisuke Kishimoto, Yichen Tong +1

We prove that the loop space of a quasitoric manifold is homotopy commutative if and only if the underlying polytope is a product of $3$ -simplices $(Δ^{3})^{n}$ and the characteristic…

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.GT2022★ 1 cited

Vector fields on non-compact manifolds

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

Let $M$ be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group $G$ . We establish a Poincaré-Hopf theorem for a bounded vector fi…

math.AT2021

Higher homotopy normalities in topological groups

Mitsunobu Tsutaya

The purpose of this paper is to introduce $N_{k} (ℓ)$ -maps ( $1 \leq k, ℓ \leq \infty$ ), which describe higher homotopy normalities, and to study their basic properties and examples. A…

math.KT2021

Hilbert bundles with ends

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and…

math.GR2021★ 1 cited

De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface

Hirokazu Maruhashi, Mitsunobu Tsutaya

We compute the de Rham cohomology of the weak stable foliation of the geodesic flow of a connected orientable closed hyperbolic surface with various coefficients. For most of the c…

math.AT2021★ 7 cited

Homotopy type of the unitary group of the uniform Roe algebra on $Z^{n}$

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

We study the homotopy type of the space of the unitary group $\U_1(C^\ast_u(|\mathbb{Z}^n|))$ of the uniform Roe algebra $C_{u}^{*} (∣ Z^{n} ∣)$ of $Z^{n}$ . We show that…

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.DS2020★ 1 cited

$G$ -index, topological dynamics and marker property

Masaki Tsukamoto, Mitsunobu Tsutaya, Masahiko Yoshinaga

Given an action of a finite group $G$ , we can define its index. The $G$ -index roughly measures a size of the given $G$ -space. We explore connections between the $G$ -index theory an…

math.AT2020★ 3 cited

Homotopy type of the space of finite propagation unitary operators on $Z$

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from the viewpoint of quantum walks in mathematical physics.…

math.AT2018

A short proof for tc(K) = 4

Norio Iwase, Michihiro Sakai, Mitsunobu Tsutaya

We show a method to determine topological complexity from the fibrewise view point, which provides an alternative proof for tc(K) = 4, where K denotes Klein bottle.

math.AT2016★ 2 cited

Higher homotopy commutativity in localized Lie groups and gauge groups

Sho Hasui, Daisuke Kishimoto, Mitsunobu Tsutaya

The first aim of this paper is to study the $p$ -local higher homotopy commutativity of Lie groups in the sense of Sugawara. The second aim is to apply this result to the $p$ -local…

math.AT2016

Coincidence Reidemeister trace and its generalization

Mitsunobu Tsutaya

We give a homotopy invariant construction of the Reidemeister trace for the coincidence of two maps between closed manifolds of not necessarily the same dimensions. It is realized…

math.AT2015★ 3 cited

Infiniteness of $A_{\infty}$ -types of gauge groups

Daisuke Kishimoto, Mitsunobu Tsutaya

Let $G$ be a compact connected Lie group and let $P$ be a principal $G$ -bundle over $K$ . The gauge group of $P$ is the topological group of automorphisms of $P$ . For fixed $G$ and…

math.AT2014★ 3 cited

Mapping spaces from projective spaces

Mitsunobu Tsutaya

We denote the $n$ -th projective space of a topological monoid $G$ by $B_{n} G$ and the classifying space by $B G$ . Let $G$ be a well-pointed topological monoid of the homotopy type of…

math.AT2014★ 6 cited

Samelson products in p-regular SO(2n) and its homotopy normality

Daisuke Kishimoto, Mitsunobu Tsutaya

A Lie group is called $p$ -regular if it has the $p$ -local homotopy type of a product of spheres. (Non)triviality of the Samelson products of the inclusions of the factor spheres in…

math.AT2012

Homotopy pullback of $A_{n}$ -spaces and its applications to $A_{n}$ -types of gauge groups

Mitsunobu Tsutaya

We construct the homotopy pullback of $A_{n}$ -spaces and show some universal property of it. As the first application, we review the Zabrodsky's result which states that for each pri…

math.AT2011★ 7 cited

Finiteness of $A_{n}$ -equivalence types of gauge groups

Mitsunobu Tsutaya

Let $B$ be a finite CW complex and $G$ a compact connected Lie group. We show that the number of gauge groups of principal $G$ -bundles over $B$ is finite up to $A_{n}$ -equivalence fo…

math.AT2011★ 3 cited

A note on homotopy types of connected components of Map(S^4,BSU(2))

Mitsunobu Tsutaya

Connected components of $\Map(S^4,B\SU(2))$ are the classifying spaces of gauge groups of principal $\SU(2)$-bundles over $S^{4}$ . Tsukuda [Tsu01] has investigated the homotopy types…

Uniform Lefschetz fixed-point theory

Morse inequalities for noncompact manifolds

Homotopy commutativity in quasitoric manifolds

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

Vector fields on non-compact manifolds

Higher homotopy normalities in topological groups

Hilbert bundles with ends

De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface

Homotopy type of the unitary group of the uniform Roe algebra on Zn

Tverberg's theorem for cell complexes

G-index, topological dynamics and marker property

Homotopy type of the space of finite propagation unitary operators on Z

A short proof for tc(K) = 4

Higher homotopy commutativity in localized Lie groups and gauge groups

Coincidence Reidemeister trace and its generalization

Infiniteness of A∞​-types of gauge groups

Mapping spaces from projective spaces

Samelson products in p-regular SO(2n) and its homotopy normality

Homotopy pullback of An​-spaces and its applications to An​-types of gauge groups

Finiteness of An​-equivalence types of gauge groups

A note on homotopy types of connected components of Map(S^4,BSU(2))

Homotopy type of the unitary group of the uniform Roe algebra on $Z^{n}$

$G$ -index, topological dynamics and marker property

Homotopy type of the space of finite propagation unitary operators on $Z$

Infiniteness of $A_{\infty}$ -types of gauge groups

Homotopy pullback of $A_{n}$ -spaces and its applications to $A_{n}$ -types of gauge groups

Finiteness of $A_{n}$ -equivalence types of gauge groups