Fundamental groups of real toric spaces over simple polytopes
The study of real toric spaces is an interesting topic. To some extent, real toric spaces are a generalization of smooth toric varieties. Compared with other manifolds, due to the special combinatorial structures of real toric spaces, some topological invariants (such as cohomology rings, characteristic classes, and so on) of real toric spaces can be computable. This enables us to obtain some profound results that are not available on other manifolds. In addition, real toric spaces can provide some concrete examples for some abstract theories about manifolds. In this article, the authors study the cubical structures and fundamental groups of real toric spaces. Specifically, they give an explicit presentation of the fundamental group of a real toric space over a simple polytope. As an application, they give a description of the existence of non-degenerate colorings on a simple polytope.
scientific article; zbMATH DE number 7615094
scientific article