The equivariant homeomorphism class of an (orientable) small cover over a simple convex polytope P^n bijectively corresponds to the equivalence class of its (orientable) coloring under the action of automorphism group of face poset of P^n. By calculating the number of orbits of group actions we determine the number of equivariant homeomorphism classes of small covers over products of a polygon with a simplex. Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.
Small cover, equivariant homeomorphism, polytope, coloring
WANG, YANYING and CHEN, YANCHANG
"Small covers over products of a polygon with a simplex,"
Turkish Journal of Mathematics: Vol. 36:
1, Article 14.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss1/14