# Poincare

## Smooth 4-dimensional Poincare conjecture ★★★★

Author(s): Poincare; Smale; Stallings

\begin{conjecture} If a $4$-manifold has the homotopy type of the $4$-sphere $S^4$, is it diffeomorphic to $S^4$? % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. \end{conjecture}

Keywords: 4-manifold; poincare; sphere