Triangulations that are not manifolds?

Question

Any differentiable manifold can be triangulated (and it can be done piecewise-linearly), but I get the impression that the converse is false. For insight, is there a good example of a topological space that can be triangulated but is not a differentiable manifold? If we know that a space can be triangulated, is there some set of additional assumptions under which we can say that it's a manifold?

Answer 1

For instance, if links in the complex are triangulated spheres, then the complex is a PL manifold. However, even if links are not spheres, the complex might still be homeomorphic to a topological manifold (the double suspension of a 3-manifold which is a homology 3-sphere is a classical example).