# 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