preprint
Orientations on simplicial complexes and cubical complexes.
by Masahiro Hachimori
Abstract
In this paper we discuss orientations of the facet-ridge incidence graphs
of regular CW complexes, especially the cases of simplicial complexes
and cubical complexes.
When the orientation is acyclic and each ridge has in-degree $\ge 1$,
it gives a covering by a family of sets associated to each facets.
We give a condition when the covering becomes a partition.
For simplicial complexes it provides
a characterization of shellability, and for cubical complexes
we derive inequalities for the Betti numbers of the complexes.
Also some additional examples are supplied.