On the Smale Conjecture for Diff$(S^4)$
Abstract: Recently Watanabe disproved the Smale Conjecture for $S4$, by showing Diff$(S{4})\neq SO(5)$. He showed this by proving that their higher homotopy groups are different. Here we prove this more directly by showing $\pi_{0}$Diff$(S{4})\neq 0$, otherwise a certain loose-cork could not possibly be a loose-cork.
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