A construction originating in work of Davis and Januszkiewicz gives an interesting "combinatorial" family of spaces which are parameterized by a finite simplicial complex and a pair of spaces. By making suitable choices, one obtains a range of familiar and less familiar spaces: classifying spaces for right-angled Artin groups, Coxeter groups, and Bestvina-Brady groups; the moment-angle complexes of Buchstaber and Panov; the complements of certain real and complex subspace arrangements. The topological invariants of some of these spaces can be described particularly explicitly, via combinatorial commutative algebra. I will describe some results of this sort, and I will attempt to promote the construction as interesting and useful. |