
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
.




Keywords: 4-sphere; diffeomorphisms
$C^r$ Stability Conjecture ★★★★
Conjecture Any
structurally stable diffeomorphism is hyperbolic.

Keywords: diffeomorphisms,; dynamical systems
