Characterization of combinatorial manifolds in terms of links I need to reference the following result. Do you know a good source?
The following conditions on an $n$-dimensional simplicial complex $S$ are equivalent:
a) $S$ is an $n$ manifold;
b) The link of every vertex of $S$ is homeomorphic to the $(n - 1)$-sphere;
c) The link of every $k$-simplex is homeomorphic to the $(n - k - 1)$-sphere.
 A: The usual term for objects like this is "combinatorial manifolds".
However, the result is not quite true as you have stated.  Definitely b is true if and only if c is true, and b implies a.  However, a does not imply b.  There definitely exist simplicial complexes which do not satisfy b or c but which are topological manifolds.  For example, the famous double suspension theorem of Cannon (weaker versions were proved by Edwards) says that if $X$ is a homology $n$-sphere, then the space $Y$ obtained by suspending $X$ twice is homeomorphic to the $(n+2)$-sphere.  If neither $X$ nor the suspension of $X$ is an actual sphere (for instance, this holds if $X$ is the Poincare homology sphere), the vertices of $Y$ corresponding to the suspension points will then not satisfy b.
A: I'm pretty sure you can find this kind of results in 
Rourke and Sanderson's "Introduction to Piecewise linear topology".
http://www.amazon.com/Introduction-Piecewise-Linear-Ergebnisse-Mathematik-Grenzgebiete/dp/0387111026
