The fundamental group of a poset and colorings of its Hasse diagram

JONATHAN ARIEL BARMAK; ELIAS GABRIEL MINIAN

Congreso; Mathematical Congress of the Americas; 2013

The fundamental group of a poset and colorings of its Hasse diagram. We introduce the notion of a coloring of a poset P with colors in a group and study some elementary problems related to this concept. We show that there is a correspondence between classes of colorings of P and normal subgroups of pi_1(P) (and therefore with the regular coverings of P). We derive a simple method for nding a (new) presentation of the fundamental group of any poset. These ideas can be then used to compute fundamental groups of arbitrary complexes. Some direct applications include a generalization of van Kampen Theorem and a characterization of posets with abelian fundamental group.