Some small orbifolds over polytopes

Abstract

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the cohomology rings of these orbifolds when the dimension of the orbifold is even. These orbifolds are intimately related to the notion of small cover.

arXiv comment19 pages, 2 figures, many changes to the previous version. Comments and suggestions are welcome