Orientable small covers over a product space

Abstract

A small cover is a closed manifold Mn with a locally standard (ℤ2)n-action such that its orbit space is a simple convex polytope Pn. Let Δn denote an n-simplex and P(m) an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space \(\Delta ^{n_1 } \times \Delta ^{n_2 } \times P(m)\), where n1 is odd.