Double suspension theorem
Introduction In geometric topology,  the '''double suspension theorem''' of James W. Cannon () and Robert D. Edwards states that the double suspension ''S''2''X'' 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 ''S''2''X'' (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. The reason is that, unlike in piecewise-linear manifolds, the link of one of the suspension points is not a sphere.
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References *** Steve Ferry,  Geometric Topology Notes (''See Chapter 26, page 166'')