Double suspension theorem

In geometric topology, the double suspension theorem of James W. Cannon (Cannon (1979)) and Robert D. Edwards states that the double suspension S2X of a homology sphere X is a topological sphere. If X is a piecewise-linear homology sphere but not a sphere, then its double suspension S2X (with a triangulation derived by applying the double suspension operation to a triangulation of X) is an example of a triangulation of a topological sphere that is not piecewise-linear.

Source: Wikipedia — Double suspension theorem (CC BY-SA 4.0)