Decompositions of polyhedral products for shifted complexes

@article{Iriye2013DecompositionsOP,
  title={Decompositions of polyhedral products for shifted complexes},
  author={Kouyemon Iriye and Daisuke Kishimoto},
  journal={Advances in Mathematics},
  year={2013},
  volume={245},
  pages={716-736}
}
Decompositions of suspensions of spaces involving polyhedral products
Two homotopy decompositions of supensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral products by Bahri,
The dual polyhedral product, cocategory and nilpotence
Characterisation of polyhedral products with finite generalised Postnikov decomposition
Abstract A generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In
Topology of polyhedral products and the Golod property of Stanley-Reisner rings
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 complex via cohomology.
Polyhedral products for simplicial complexes with minimal Taylor resolutions
We prove that for a simplicial complex $K$ whose Taylor resolution for the Stanley-Reisner ring is minimal, the following four conditions are equivalent: (1) $K$ satisfies the strong gcd-condition;
Higher order Massey products and applications
In this survey, we discuss two research areas related to Massey’s higher operations. The first direction is connected with the cohomology of Lie algebras and the theory of representations. The second
Toric homotopy theory
These notes describe some of the homotopy theory surrounding Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. These spaces are defined by gluing
Polyhedral products and features of their homotopy theory
A polyhedral product is a natural subspace of a Cartesian product that is specified by a simplicial complex. The modern formalism arose as a generalization of the spaces known as moment-angle
...
1
2
3
4
...

References

SHOWING 1-10 OF 16 REFERENCES
Colorings of simplicial complexes and vector bundles over Davis–Januszkiewicz spaces
We show that coloring properties of a simplicial complex K are reflected by splitting properties of a bundle over the associated Davis–Januszkiewicz space whose Chern classes are given by the
Moment-angle Complexes, Monomial Ideals and Massey Products
Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of
Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products
We compute: * the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), Bestvina-Brady groups, and graph products of groups, * the L^2-Betti
Rational Homotopy of the Polyhedral Product Functor
Let (X, *) be a pointed CW-complex, K be a simplicial complex on n vertices and X-K be the associated polyhedral power. In this paper, we construct a Sullivan model of XK from K and from a model of
Pull-Backs in Homotopy Theory
The (based) homotopy category consists of (based) topological spaces and (based) homotopy classes of maps. In these categories, pull-backs and push-outs do not generally exist. For example, no
Convex polytopes, Coxeter orbifolds and torus actions
0. Introduction. An n-dimensional convex polytope is simple if the number of codimension-one faces meeting at each vertex is n. In this paper we investigate certain group actions on manifolds, which
Torus Actions and their Applications in Topology and Combinatorics
Here, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and
...
1
2
...