Homology, Homotopy and Applications
Volume 18 (2016)
A note on coverings of posets, $A$-spaces and polyhedra
Pages: 143 – 150
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.
covering map, simplicial complex, poset, $A$-space
2010 Mathematics Subject Classification
06A07, 18B35, 55U10, 57M10