Bing's recognition theorem

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In topology, a branch of mathematics, Bing's recognition theorem, named for R. H. Bing, asserts that a necessary and sufficient condition for a 3-manifold M to be homeomorphic to the 3-sphere is that every Jordan curve in M be contained within a topological ball. It is a weak version of the Poincaré conjecture.

References

Bing, R. H. (1958). "Necessary and sufficient conditions that a 3-manifold be $S 3$ ". Annals of Mathematics. Second Series. 68 (1): 17–37. doi:10.2307/1970041. MR 0095471. Zbl 0081.39202. (Erratum: doi:10.2307/1970205)
Hempel, John (1976). 3-Manifolds. Annals of Mathematics Studies. Vol. 86. Princeton, NJ: Princeton University Press. doi:10.1090/chel/349. MR 0415619. Zbl 0345.57001.
Rolfsen, Dale (1990). Knots and links. Mathematics Lecture Series. Vol. 7 (Corrected reprint of the 1976 original ed.). Houston, TX: Publish or Perish, Inc. doi:10.1090/chel/346. ISBN 0-914098-16-0. MR 1277811. Zbl 0854.57002.

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