Bing's recognition theorem

Short description: On when a 3-manifold is homeomorphic to the 3-sphere

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 S³". Annals of Mathematics. Second Series 68 (1): 17–37. doi:10.2307/1970041.  (Erratum: doi:10.2307/1970205)
• Hempel, John (1976). 3-Manifolds. Annals of Mathematics Studies. 86. Princeton, NJ: Princeton University Press. doi:10.1090/chel/349. 
• Rolfsen, Dale (1990). Knots and links. Mathematics Lecture Series. 7 (Corrected reprint of the 1976 original ed.). Houston, TX: Publish or Perish, Inc.. doi:10.1090/chel/346. ISBN 0-914098-16-0.