Small covers over products of a polygon with a simplex (Q2892205)

A small cover is a closed smooth manifold \(M\) of dimension \(n\) with a smooth effective \(({\mathbb Z}_2)^n\)-action such that the action is locally isomorphic to a standard \(({\mathbb Z}_2)^n\)-representation on \({\mathbb R}^n\) and the orbit space is homeomorphic to a simple convex polytope. The notion of a small cover as a real topological version of toric variety was introduced by \textit{M. W. Davis} and \textit{T. Januszkiewicz} in [Duke Math J. 62, No. 2, 417--451 (1991; Zbl 0733.52006)]. The paper under review studies the equivariant classification of small covers over products of a polygon and a simplex. The authors determine the number of equivariant homeomorphism classes of such small covers. In particular, the number in the orientable case is also determined.