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Mar 12, 2019 at 19:44 comment added Ryan Budney A little more detail on Watanabe's paper: There is an equivalence $Diff(S^n) \simeq O_{n+1} \times Diff(D^n)$. Watanabe argues $\pi_i Diff(D^4)$ is non-trivial for $i \geq 1$. The $i=0$ case is closely connected to the 4-dimensional Schoenflies problem. At present it does not appear Watanabe's argument says anything about the $i=0$ case.
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Mar 12, 2019 at 16:59 history answered Thomas Alexander Chansler CC BY-SA 4.0