Suppose one has a Morse matching (acyclic matching) of a poset $P$ of rank $n$ in which the only unmatched cells are 0-cells and $(n-1)$-cells, the same number $k$ of each one.
Can I conclude that the simplicial complex associated to $P$ is the disjoint union of spheres?
I know that if one has only one 0-cell (and the some number of $(n-1)$-cells) then the complex would be a wedge of spheres, so I was wondering what would happen if one has more than one 0-cell.