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Smale, S.
What is the homotopy type of the group of diffeomorphisms of the 4-sphere? ★★★★
Author(s): Smale
Problem
has the homotopy-type of a product space
where
is the group of diffeomorphisms of the 4-ball which restrict to the identity on the boundary. Determine some (any?) homotopy or homology groups of
.
![$ Diff(S^4) $](/files/tex/18446359b22efa9d172da85f2cb353a1171ad1d9.png)
![$ Diff(S^4) \simeq \mathbb O_5 \times Diff(D^4) $](/files/tex/ad3d9f988825524617e3f752930a949f55807846.png)
![$ Diff(D^4) $](/files/tex/c7557ce04e95c8a9a974f0043bddb280c65324d3.png)
![$ Diff(D^4) $](/files/tex/c7557ce04e95c8a9a974f0043bddb280c65324d3.png)
Keywords: 4-sphere; diffeomorphisms
$C^r$ Stability Conjecture ★★★★
Conjecture Any
structurally stable diffeomorphism is hyperbolic.
![$ C^r $](/files/tex/20f43cb190c38dfabfa818a8770413f83ef84acd.png)
Keywords: diffeomorphisms,; dynamical systems
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