In a triangulation of a general topological space, we can define a face link (for any face in the triangulation). Intuitively, this is a kind of "$\epsilon-$sphere" in metric space.
In chapter 3.8 of Stanley's enumerative combinatorics is stated that for any nonempty face of a triangulation of manifold (with or w/o boundary) it is well-known that the homology group of the link of this face should be the same as a sphere or ball.
Well, at least now, I can't find a little hint to prove this, and unfortunately, Stanley's book did not suggest any reference to this result.
Is there anyone who gives a comment to this result? Any little one would be appreciated.