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

Jonathan Ariel Barmak; Elias Gabriel Minian

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arXiv · 1212.6442

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

Jonathan Ariel Barmak·Elias Gabriel Minian

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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.

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Jonathan Ariel Barmak, Elias Gabriel Minian. 2014-12-15. $G$-colorings of posets, coverings and presentations of the fundamental group. https://arxiv.org/abs/1212.6442

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