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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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What is the status of the 4-dimensional Smale Conjecture?
4-dimensional Smale conjecture claims the following:
The inclusion $SO(5)$ → $SDiff(S^4)$ is a homotopy equivalence.
or Does $Diff(S^4)$ have the homotopy-type of $O(5)$ ?.
The inclusion $SO(n + 1$ …