## 40 Citations

Decompositions of suspensions of spaces involving polyhedral products

- Mathematics
- 2015

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,…

Characterisation of polyhedral products with finite generalised Postnikov decomposition

- Mathematics
- 2020

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

- Mathematics
- 2013

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

- Mathematics
- 2015

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

- MathematicsTopology, Geometry, and Dynamics
- 2021

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

- Mathematics
- 2017

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

- MathematicsHandbook of Homotopy Theory
- 2020

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…

## References

SHOWING 1-10 OF 16 REFERENCES

Colorings of simplicial complexes and vector bundles over Davis–Januszkiewicz spaces

- Mathematics
- 2009

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

- Mathematics
- 2007

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

- Mathematics
- 2010

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

- Mathematics
- 2008

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…

The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces

- Mathematics
- 2007

Pull-Backs in Homotopy Theory

- MathematicsCanadian Journal of Mathematics
- 1976

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

- Mathematics
- 1991

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

- Mathematics
- 2002

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…