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Timeline for Homotopy of group actions

Current License: CC BY-SA 4.0

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Mar 15, 2019 at 20:38 vote accept Ali Taghavi
Mar 13, 2019 at 23:54 history edited Denis Nardin CC BY-SA 4.0
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Mar 13, 2019 at 22:55 comment added Denis Nardin Also, if I'm not mistaken, question 1 is true for any action, since $S^1$ is a connected Lie group (so for every $g$, $\alpha_g$ is homotopic to the identity...)
Mar 13, 2019 at 22:54 history edited Denis Nardin CC BY-SA 4.0
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Mar 13, 2019 at 22:47 comment added Denis Nardin @YCor Sorry, the addition of $G=S^1$ was later. Will amend my answer (pretty much the same thing works, of course)
Mar 13, 2019 at 22:26 comment added YCor This answers the second question. For the first, just take $n\ge 2$ and choose the nontrivial action using a element of order 2 and determinant 1.
Mar 13, 2019 at 22:00 history edited Denis Nardin CC BY-SA 4.0
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Mar 13, 2019 at 21:47 history answered Denis Nardin CC BY-SA 4.0