31 citations · 69 across the 17 of their papers we have counts for
17 papers
Tight complexes are Golod
Kouyemon Iriye, Daisuke Kishimoto
The Golodness of a simplicial complex is defined algebraically in terms of the Stanley-Reisner ring, and it has been a long-standing problem to find its combinatorial characterizat…
Golod and tight 3-manifolds
Kouyemon Iriye, Daisuke Kishimoto
The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations,…
Two-dimensional Golod complexes
Kouyemon Iriye, Daisuke Kishimoto
We characterize two-dimensional Golod complexes combinatorially by vertex-breakability and topologically by the fat-wedge filtration of a polyhedral product. Applying the character…
Characterisation of polyhedral products with finite generalised Postnikov decomposition
Kouyemon Iriye, Daisuke Kishimoto, Ran Levi
A generalised Postnikov tower for a space is a tower of principal fibrations with fibres generalised Eilenberg-MacLane spaces, whose inverse limit is weakly homotopy equivalent…
Whitehead products in moment-angle complexes
Kouyemon Iriye, Daisuke Kishimoto
In toric topology, to a simplicial complex with vertices, one associates two spaces, the moment-angle complex and the Davis-Januszkiewicz space . Thes…
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…
On the moment-angle manifold constructed by Fan, Chen, Ma and Wang
Kouyemon Iriye
Fan, Chen, Ma and Wang constructed a moment-angle manifold whose cohomology ring is isomorphic to that of a connected sum of sphere products with one product of three spheres…
A Golod complex with non-suspension moment-angle complex
Kouyemon Iriye, Tatsuya Yano
It could be expected that the moment-angle complex associated with a Golod simplicial complex is homotopy equivalent to a suspension space. In this paper, we provide a counter exam…
Golodness and polyhedral products for two dimensional simplicial complexes
Kouyemon Iriye, Daisuke Kishimoto
Golodness of 2-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topoogical characterization of Golodness of surface triangulations is…
Polyhedral products for simplicial complexes with minimal Taylor resolutions
Kouyemon Iriye, Daisuke Kishimoto
We prove that for a simplicial complex whose Taylor resolution for the Stanley-Reisner ring is minimal, the following four conditions are equivalent: (1) satisfies the stro…
Polyhedral products for shifted complexes and higher Whitehead products
Kouyemon Iriye, Daisuke Kishimoto
This paper studies the map between polyhedral products induced from the pinch maps $(CX_i,X_i)\to(ΣX…
Decompositions of suspensions of spaces involving polyhedral products
Kouyemon Iriye, Daisuke Kishimoto
Two homotopy decompositions of supensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral…
Fat wedge filtrations and decomposition of polyhedral products
Kouyemon Iriye, Daisuke Kishimoto
The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex is studied by investigating its filtration called the fat wedge…
Homotopy decomposition of diagonal arrangements
Daisuke Kishimoto, Kouyemon Iriye
Given a space and a simplicial complex with -vertices, the arrangement of partially diagonal subspaces of , called the dragonal arrangement, is defined. We decompos…
Topology of polyhedral products and the Golod property of Stanley-Reisner rings
Kouyemon Iriye, Daisuke Kishimoto
The polyhedral product is a space constructed from a simplicial complex and a collection of pairs of spaces, which is connected with the Stanley Reisner ring of the simplicial comp…
Wedge decomposition of polyhedral products
Kouyemon Iriye, Daisuke Kishimoto
We prove that certain polyhedral products, including the moment-angle complexes, for the Alexander duals of shellable and sequentially Cohen-Macaulay complexes decompose into wedge…
On the Gray index conjecture for phantom maps
Kouyemon Iriye
We study the Gray index of phantom maps, which is a numerical invariant of phantom maps. It is conjectured that the only phantom map with infinite Gray index between finite-type sp…