title: Double suspension theorem
text: # 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 $S^2X$ 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 $S^2X$ (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.
  
  