Isotopy of orientation-preserving diffeomorphisms of the 4-sphere

Let f ⁣:S4S4f\colon S^4\to S^4 be an orientation-preserving self-diffeomorphism. Smale conjecture, special case. Every orientation-preserving self-diffeomorphism of S4S^4 is smoothly isotopic to the identity. This is presented as an important case that remains open, concerning the mapping class group of the 4-sphere.

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Primary source

Jianfeng Lin and Anubhav Mukherjee, “Family Bauer–Furuta invariant, Exotic Surfaces and Smale conjecture”, arXiv:2110.09686 (2021).

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