MomentAngleComplex -- the class of all moment-angle complexes

Given a simplicial complex $K$ on $m$ vertices, the moment-angle complex $\mathcal{Z}_K$ is a cellular complex constructed as a union of certain products of disks and circles: $$\mathcal{Z_K} = \bigcup_{\sigma \in K} \left( (D^2)^\sigma \times (S^1)^{[m] \setminus \sigma} \right).$$ These spaces admit a natural action of the torus $T^m = (S^1)^m$. Non-singular toric varieties (not necessarily complete) are homotopy equivalent to partial quotients of moment-angle complexes by freely acting subtori of $T^m$. Thus, moment-angle complexes are an important class of spaces studied in Toric Topology. Their topological properties can be determined from the combinatorics of the underlying simplicial complex. This package implements methods to determine some of these properties. A moment-angle complex is a special case of polyhedral products.