This chapter reviews the various fundamental unstable and stable splitting theorems for the
polyhedral product. It presents results on the cohomology of polyhedral products. The …

Toric topology emerged in the end of the 1990s on the borders of equivariant topology,
algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly …

A moment-angle complex Z_K is a compact topological space associated with a finite
simplicial complex K. It is realized as a subspace of a polydisk (D^2)^m, where m is the …

We extend the construction of moment-angle complexes to simplicial posets by associating
a certain T m-space ZS to an arbitrary simplicial poset S on m vertices. Face rings ℤ [S] of …

In this article, we prove that Buchstaber invariant of 4-dimensional real universal complex is
no less than 24 as a follow-up to the work of Ayzenberg and Sun. Moreover, a lower bound …

We consider an operation K↦ L (K) on the set of simplicial complexes, which we call the
“doubling operation.” This combinatorial operation was recently introduced in toric topology …

In this paper, we define a simplicial complement ℙ={σ 1, σ 2,..., σ s} to be a sequence of
subsets of [m] and prove that the simplicial complement ℙ corresponds to an unique …

Any finite simplicial complex K and a partition of the vertex set of K determines a canonical
quotient space of the moment-angle complex of \mathcalK. We prove that the cohomology …

We consider an operation K\to L (K) on the set of simplicial complexes, which we call the"
doubling operation". This combinatorial operation has been recently brought into toric …

Изучение действий групп на различных топологических пространствах является клас
сической и обширной областью алгебраической топологии. В последние десятилетия …