TITLE: What's the difference between a PL simplicial sphere and a shellable simplicial sphere?
QUESTION [8 upvotes]: Shellability of a simplicial sphere tells us that we can build up the complex one facet at a time such that at each step (except the last step) the complex is a PL-ball. At the last step it is of course a PL-sphere.
Lickorish showed that there exist non-shellable d-spheres for $d \geq 3$.
My question, perhaps a cynical one, is 'Are there any practical implications for why someone would care to have a shellable simplicial sphere, rather than just a PL-sphere?

REPLY [2 votes]: I think the question is slightly missing the point, in a way that it may be useful to explain. Frequently, the reason you would want to show something is a shellable simplicial sphere is in order to be able to deduce that it is a sphere at all. Given some crazy simplicial complex, it is not obvious whether it is a sphere or not, but for a shellable complex, it's much easier to tell.