Timeline for nontrivial $\pi_2(\textrm{Diff}(M))$

13 events

when toggle format	what		by	license	comment
Jun 17, 2021 at 8:02	history	edited	Sam Nead	CC BY-SA 4.0	formatting
Jun 17, 2021 at 7:25	answer	added	Ryan Budney		timeline score: 5
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Feb 15, 2014 at 14:27	history	edited	user9072		edited tags
May 26, 2012 at 8:36	history	edited	Mircea	CC BY-SA 3.0	edited title
May 25, 2012 at 20:41	comment	added	Tom Goodwillie		By the way, since $\pi_2$ of a Lie group is always trivial the fact that $\pi_2Diff(M)$ can be nontrivial is especially striking.
May 25, 2012 at 20:39	comment	added	Tom Goodwillie		See Hatcher's expanded answer and the comments to it.
May 25, 2012 at 15:48	answer	added	Vitali Kapovitch		timeline score: 13
May 24, 2012 at 12:03	vote	accept	Mircea
May 24, 2012 at 12:03	comment	added	Mircea		Thanks! so what is a guess of a suitable n?
May 24, 2012 at 11:26	answer	added	Allen Hatcher		timeline score: 43
May 24, 2012 at 11:08	comment	added	André Henriques		My guess is that there exists an $n$ such that the diffeomorphism group of the $n$-sphere has non-trivial $\pi_2$. E.g. the orientation preserving diffeomorphism group of $S^6$ has non-trivial $\pi_0$, as witnessed by the existence of exotic 7-spheres. So I don't see any reason for $\pi_2$ to always vanish.
May 24, 2012 at 10:29	history	asked	Mircea	CC BY-SA 3.0