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Feb 23, 2016 at 10:49 comment added Sebastian Goette @StevenStadnicki Of course. Any example with a symmetry without fixpoints would do the job.
Feb 23, 2016 at 0:09 comment added Steven Stadnicki Wouldn't it be easier to just point out the example of a point and its antipode?
Feb 18, 2016 at 15:00 history edited Sebastian Goette CC BY-SA 3.0
Followed Dirk's suggestions ...
Feb 18, 2016 at 14:57 comment added Dirk I got slightly confused by $S^n$ denoting the unit sphere by $S_n$ denoting the symmetric group… Oh, by the way: The $\gamma(x)$ should be $\gamma(p)$, I guess? In view of Peter Michor's answer you may rephrase "There cannot be a meaningful unique centroid…".
Feb 18, 2016 at 13:53 history answered Sebastian Goette CC BY-SA 3.0