A note on coverings of posets, A-spaces and polyhedra.

JONATHAN ARIEL BARMAK; ELIAS GABRIEL MINIAN

HOMOLOGY, HOMOTOPY AND APPLICATIONS (HHA)

INT PRESS BOSTON, INC

Año: 2016 vol. 18 p. 143 - 150

1532-0073

We show that there exists a correspondence between the equivalence classes of coverings of a polyhedron and the equivalence classes of coverings of its poset of simplices. The same is true for a poset and its order complex. The coverings of a poset can be understood in two equivalent ways, as categorical coverings, when the poset is viewed as a category, or as topological coverings, when it is viewed as an A-space. This implies that the theory of coverings of polyhedra can be handled completely in thecombinatorial setting.