Double suspension theorem

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Short description: The double suspension of a homology sphere is a topological sphere

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.[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.

See also

  • Disjoint discs property (ru)

References

  1. Robert D. Edwards, "Suspensions of homology spheres" (2006) ArXiv (reprint of private, unpublished manuscripts from the 1970's)
  2. Robert 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. James W. Cannon, "Σ2 H3 = S5 / G", Rocky Mountain J. Math. (1978) 8, pp. 527-532.