Takahiro Matsushita

activity

20122026

most citedFundamental groups of neighborhood complexes

6 citations · 22 across the 28 of their papers we have counts for

collaborators

31 papers

math.CO2026

Cayley graphs of abelian groups, circular colorings and discrete fundamental groups

Kengo Enami, Takahiro Matsushita

For each integer $k \geq 2$ , we prove that an abelian group $Γ$ satisfies $exp (Γ) \in {1, \dots, k} \cup {2, 4, \dots, 2 k}$ if and only if it admits no non-bipartite Cayley graph wh…

math.GR2023

Coarse group theoretic study on stable mixed commutator length

Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2

Let $G$ be a group and $N$ a normal subgroup of $G$ . We study the large scale behavior, not the exact values themselves, of the stable mixed commutator length $sc l_{G, N}$ on the mi…

math.AT2023

Van Kampen-Flores theorem and Stiefel-Whitney classes

Daisuke Kishimoto, Takahiro Matsushita

The van Kampen-Flores theorem states that the $d$ -skeleton of a $(2 d + 2)$ -simplex does not embed into $R^{2 d}$ . We prove the van Kampen-Flores theorem for triangulations of…

math.GR2022

Survey on invariant quasimorphisms and stable mixed commutator length

Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2

A homogeneous quasimorphism $ϕ$ on a normal subgroup $N$ of $G$ is said to be $G$ -invariant if $ϕ (g x g^{- 1}) = ϕ (x)$ for every $g \in G$ and for every $x \in N$ . Invariant quasimorp…

math.AT2022

Independence complexes of $(n \times 6)$ -grid graphs

Takahiro Matsushita, Shun Wakatsuki

We determine the homotopy types of the independence complexes of the $(n \times 6)$ -square grid graphs. In fact, we show that these complexes are homotopy equivalent to wedges of s…

math.AT2022

Independence complexes of $(n \times 4)$ and $(n \times 5)$ -grid graphs

Takahiro Matsushita, Shun Wakatsuki

We determine the homotopy types of the independence complexes of $(n \times 4)$ and $(n \times 5)$ -square grid graphs. In fact, they are homotopy equivalent to wedges of spheres.

math.GT2022

Invariant quasimorphisms for groups acting on the circle and non-equivalence of SCL

Shuhei Maruyama, Takahiro Matsushita, Masato Mimura

We construct invariant quasimorphisms for groups acting on the circle. Furthermore, we provide a criterion for the non-extendablity of the resulting quasimorphisms and an explicit…

math.GR2022

Mixed commutator lengths, wreath products and general ranks

Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2

In the present paper, for a pair $(G, N)$ of a group $G$ and its normal subgroup $N$ , we consider the mixed commutator length $cl_{G, N}$ on the mixed commutator subgroup $[…

math.AT2021

Jacobi identity in polyhedral products

Daisuke Kishimoto, Takahiro Matsushita, Ryusei Yoshise

We show that a relation among minimal non-faces of a fillable complex $K$ yields an identity of iterated (higher) Whitehead products in a polyhedral product over $K$ . In particular…

math.AT2021

Van Kampen-Flores theorem for cell complexes

Daisuke Kishimoto, Takahiro Matsushita

The van Kampen-Flores theorem states that the $n$ -skeleton of a $(2 n + 2)$ -simplex does not embed into $R^{2 n}$ . We give two proofs for its generalization to a continuous ma…

math.GR2021

The space of non-extendable quasimorphisms

Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2

For a pair $(G, N)$ of a group $G$ and its normal subgroup $N$ , we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$ . To treat this space, we esta…

math.SG2021★ 2 cited

Commuting symplectomorphisms on a surface and the flux homomorphism

Morimichi Kawasaki, Mitsuaki Kimura, Takahiro Matsushita +1

Let $(S, ω)$ be a closed connected oriented surface whose genus $l$ is at least two equipped with a symplectic form. Then we show the vanishing of the cup product of the fluxes of c…

math.CO2020

Dominance complexes and vertex cover numbers of graphs

Takahiro Matsushita

The dominance complex $D (G)$ of a simple graph $G = (V, E)$ is the simplicial complex consisting of the subsets of $V$ whose complements are dominating. We show that the connectivit…

math.CO2020

Graphs whose Kronecker covers are bipartite Kneser graphs

Takahiro Matsushita

We show that there are $k$ simple graphs whose Kronecker covers are isomorphic to the bipartite Kneser graph $H (n, k)$ , and that their chromatic numbers coincide with $χ(K(n,k)) = n…

math.GR2020

Bavard's duality theorem for mixed commutator length

Morimichi Kawasaki, Mitsuaki Kimura, Takahiro Matsushita +1

Let $N$ be a normal subgroup of a group $G$ . A quasimorphism $f$ on $N$ is $G$ -invariant if $f (g x g^{- 1}) = f (x)$ for every $g \in G$ and every $x \in N$ . The goal in this paper is…

math.CO2020★ 1 cited

Independence complexes of hypergraphs and bounded degree complexes

Takahiro Matsushita

The bounded degree complex $B D (G, λ)$ is a generalization of the matching complexes of a graph. In this paper, we show that the bounded degree complex of a forest is shellable, by u…

math.CO2019

Matching complexes of polygonal line tilings

Takahiro Matsushita

The matching complex of a simple graph $G$ is a simplicial complex consisting of the matchings on $G$ . Jelić Milutinović et al. studied the matching complexes of the polygonal line…

math.AT2019

Relative phantom maps and rational homotopy

Daisuke Kishimoto, Takahiro Matsushita

We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the $lim^{1}$ and the profinite comp…

math.CO2018★ 1 cited

Matching complexes of small grids

Takahiro Matsushita

The matching complex $M (G)$ of a simple graph $G$ is the simplicial complex consisting of the matchings on $G$ . The matching complex $M (G)$ is isomorphic to the independence comple…

math.AT2017★ 3 cited

Relative phantom maps

Kouyemon Iriye, Daisuke Kishimoto, Takahiro Matsushita

The de Bruijn-Erdős theorem states that the chromatic number of an infinite graph equals the maximum of the chromatic numbers of finite subgraphs. Such a determinativeness by finit…

math.AT2016★ 1 cited

Loop space construction of bigraphs and box complexes

Takahiro Matsushita

Dochtermann introduced the loop space construction of a based graph $(G, v)$ whose basepoint is a looped vertex. He showed that the complex $C (Ω (G, v))$ is homotopy equivalent to the…

math.AT2016

Box complexes and homotopy theory of graphs

Takahiro Matsushita

We introduce a model structure on the category of graphs, which is Quillen equivalent to the category of $Z_{2}$ -spaces. A weak equivalence is a graph homomorphism which ind…

math.CO2015★ 2 cited

Homotopy types of Hom complexes of graphs

Takahiro Matsushita

The Hom complex $Hom (T, G)$ of graphs is a CW-complex associated to a pair of graphs $T$ and $G$ , considered in the graph coloring problem. It is known that certain homotopy i…

math.AT2014★ 1 cited

Some examples of non-tidy spaces

Takahiro Matsushita

We construct a free $Z_{2}$ -manifold $X_{n}$ for a positive integer $n$ such that $w_{1} (X_{n})^{n} \neq = 0$ , but there is no $Z_{2}$ -equivariant map from $S^{2}$ to $X_{n}$ .

Cayley graphs of abelian groups, circular colorings and discrete fundamental groups

Coarse group theoretic study on stable mixed commutator length

Van Kampen-Flores theorem and Stiefel-Whitney classes

Survey on invariant quasimorphisms and stable mixed commutator length

Independence complexes of (n×6)-grid graphs

Independence complexes of (n×4) and (n×5)-grid graphs

Invariant quasimorphisms for groups acting on the circle and non-equivalence of SCL

Mixed commutator lengths, wreath products and general ranks

Jacobi identity in polyhedral products

Van Kampen-Flores theorem for cell complexes

The space of non-extendable quasimorphisms

Commuting symplectomorphisms on a surface and the flux homomorphism

Dominance complexes and vertex cover numbers of graphs

Graphs whose Kronecker covers are bipartite Kneser graphs

Bavard's duality theorem for mixed commutator length

Independence complexes of hypergraphs and bounded degree complexes

Matching complexes of polygonal line tilings

Relative phantom maps and rational homotopy

Matching complexes of small grids

Relative phantom maps

Loop space construction of bigraphs and box complexes

Box complexes and homotopy theory of graphs

Homotopy types of Hom complexes of graphs

Some examples of non-tidy spaces

Independence complexes of $(n \times 6)$ -grid graphs

Independence complexes of $(n \times 4)$ and $(n \times 5)$ -grid graphs