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

Elias Gabriel Minian; Jonathan Ariel Barmak

arxiv: 1212.6442 · v2 · pith:46OADGRTnew · submitted 2012-12-28 · 🧮 math.AT · math.CO

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

Jonathan Ariel Barmak , Elias Gabriel Minian This is my paper

classification 🧮 math.AT math.CO

keywords coloringsgroupfundamentalposetspresentationscoloringconcreteconsists

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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.

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Regular coverings and fundamental groupoids of Alexandroff spaces
math.AT 2019-07 unverdicted novelty 5.0

Fundamental groupoid of Alexandroff space X is naturally isomorphic to localization of its thin specialization-preorder category; regular coverings are represented by morphism-inverting functors extending Minian-Barmak.