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Feb 10, 2015 at 14:20 comment added Robert Bryant @LennartMeier: I believe the symbol $\simeq$ in your remark denotes 'homotopy equivalence'. Is this correct?
Feb 10, 2015 at 13:53 comment added Lennart Meier As a remark: $Diff(S^2) \simeq O(3)$ (Smale) and $Diff(S^3) \simeq O(4)$ (Hatcher)
Feb 8, 2015 at 13:42 comment added მამუკა ჯიბლაძე Very interesting, thank you very much! Reading your answer I thought (seemingly unrelatedly) about yet another possibility but still am not sure whether to include it in the question. You see, in principle this might not even be a group - rather, having in mind highly connective covers of Lie groups, one might think of maps "linear up to homotopy", together with chosen such "linearizing homotopies".
Feb 8, 2015 at 12:40 history answered Robert Bryant CC BY-SA 3.0