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.[1][2]

References

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  1. ^ 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.
  2. ^ Hartnett, Kevin (September 9, 2021). "New Math Book Rescues Landmark Topology Proof". Quanta Magazine.

Sources

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