Abstract

A polyhedral product is a natural topological subspace of a Cartesian product, determined by a simplicial complex K and a family of pointed pairs of spaces (X _i , A _i ), one for each vertex of K. As noted in [126], in the special case that A _i is a basepoint for X _i , the polyhedral product mediates between the product X ₁ × X ₂ × · · · × X _m when K is the full (m − 1)-simplex, and the wedge X ₁∨X ₂∨ · · · ∨X _m when K consists of m discrete points.