In the area of mathematics known as differential topology, the disc theorem of Palais (1960) states that two embeddings of a closed k-disc into a connected n-manifold are ambient isotopic provided that if k = n the two embeddings are equioriented.
The disc theorem implies that the connected sum of smooth oriented manifolds is well defined.
A different although related and similar named result is the disc embedding theorem proved by Freedman in 1982.
References
- Freedman, Michael Hartley (1982). "The topology of four-dimensional manifolds". Journal of Differential Geometry. 17 (3): 357–453. doi:10.4310/jdg/1214437136. ISSN 0022-040X.
- Hartnett, Kevin (September 9, 2021). "New Math Book Rescues Landmark Topology Proof". Quanta Magazine.
Sources
- Palais, Richard S. (1960), "Extending diffeomorphisms", Proceedings of the American Mathematical Society, 11: 274–277, doi:10.2307/2032968, ISSN 0002-9939, JSTOR 2032968, MR 0117741
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