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.



Characterization of combinatorial manifolds in terms of links
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](http://en.wikipedia.org/wiki/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](http://en.wikipedia.org/wiki/Poincar%C3%A9_homology_sphere#Poincar.C3.A9_homology_sphere)), the vertices of $Y$ corresponding to the suspension points will then not satisfy b.


