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.[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

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 Robert D. Edwards, "Suspensions of homology spheres" (2006) ArXiv (reprint of private, unpublished manuscripts from the 1970's)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.
  • Cannon, James W. (1979), "Shrinking cell-like decompositions of manifolds. Codimension three", Annals of Mathematics, Second Series, 110 (1): 83–112, doi:10.2307/1971245, ISSN 0003-486X, MR 0541330
  • Latour, François (1979), "Double suspension d'une sphère d'homologie [d'après R. Edwards]", Séminaire Bourbaki vol. 1977/78 Exposés 507–524, Lecture Notes in Math. (in French), vol. 710, Berlin, New York: Springer-Verlag, pp. 169–186, doi:10.1007/BFb0069978, ISBN 978-3-540-09243-8, MR 0554220
  • Steve Ferry, Geometric Topology Notes (See Chapter 26, page 166)
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