Topology and Geometric Group Theory Seminar
Certain subspaces of a product of spaces whose factors are labeled by the vertices of a simplicial complex are referred to as "polyhedral product spaces". Polyhedral products are given by taking the union of subproducts depending on the face category of a fixed simplicial complex on $m$ vertices and a labelled family of $m$ topological pairs. Such polyhedral products are realized by objects studied in combinatorics, commutative algebra and algebraic geometry. Real moment-angle complexes, where the pairs are intervals and their boundaries, play a key role. We will study how the cohomology ring of real moment-angle complexes can be given in terms of the underlying simplicial complex.