$G$-colorings of posets, coverings and presentations of the fundamental group

Abstract

We introduce the notion of a coloring of a poset, which consists of a labeling of the edges in its Hasse diagram by elements in a given group $G$. We use $G$-colorings to describe the covering maps of posets and present a new method based on colorings to obtain concrete and simple presentations of the fundamental group of polyhedra.

We improved the presentation and split the paper into two parts. This part is devoted to the study of coverings and the fundamental group in terms of colorings. The second part is devoted to the study of the second homotopy group and asphericity

Cited by in corpus (4)

• On homology of finite topological spaces
• Regular coverings and fundamental groupoids of Alexandroff spaces
• The second homotopy group in terms of colorings of locally finite models and new results on asphericity
• A (co)homology theory for some preordered topological spaces