Homology, Homotopy and Applications

Volume 18 (2016)

Number 1

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

Pages: 143 – 150

DOI: https://dx.doi.org/10.4310/HHA.2016.v18.n1.a8

Authors

Jonathan Ariel Barmak (Departamento de Matemática – IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina)

Elias Gabriel Minian (Departamento de Matemática – IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina)

Abstract

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 the combinatorial setting.

Keywords

covering map, simplicial complex, poset, $A$-space

2010 Mathematics Subject Classification

06A07, 18B35, 55U10, 57M10

Published 31 May 2016