Some small orbifolds over polytopes

TL;DR

This paper introduces specific compact orbifolds derived from polytopes, computes their fundamental and homology groups, and explores their cohomology rings, linking them to small cover theory.

Contribution

It presents new classes of orbifolds over polytopes, with detailed algebraic topological invariants and connections to small cover concepts.

Findings

Computed orbifold fundamental groups and homology groups.

Determined cohomology rings for even-dimensional cases.

Established relationships between these orbifolds and small covers.

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.