Double suspension theorem

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In geometric topology, the double suspension theorem of Cannon (1979) and R. D. Edwards states that the double suspension S2X of a homology sphere X is a topological sphere.[1][2][3]

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. The reason is that, unlike in piecewise-linear manifolds, the link of one of the suspension points is not a sphere.

References[edit]

  1. ^ Robert D. Edwards, "Suspensions of homology spheres" (2006) ArXiv (reprint of private, unpublished manuscripts from the 1970's)
  2. ^ R.D. Edwards, "The topology of manifolds and cell-like maps", Proceedings of the International Congress of Mathematicians, Helsinki, 1978 ed. O. Lehto, Acad. Sci. Fenn (1980) pp 111-127.
  3. ^ J.W. Cannon, "Σ2 H3 = S5 / G", Rocky Mountain J. Math. (1978) 8, pp. 527-532.