Timeline for Does there exist a free action of $\mathbb Z_p$ on this space?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 4, 2019 at 15:59 | history | edited | Shivani Sengupta | CC BY-SA 4.0 |
edited title
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| Nov 20, 2018 at 18:07 | vote | accept | Shivani Sengupta | ||
| Nov 19, 2018 at 22:01 | answer | added | Will Sawin | timeline score: 8 | |
| Nov 19, 2018 at 18:43 | comment | added | abx | @ Nick L: These automorphisms have order 2, and this is excluded in the question. LFPT tells you immediately that an an automorphism of $\mathbb{CP}^n$ of odd prime order has fixed points. However this is not so clear (to me) in the product case. | |
| Nov 19, 2018 at 18:27 | comment | added | Nick L | @Will Sawin, could you explain more? Every $\mathbb{CP}^{n}$ with $n$ odd has a fixed point free self homeomorphism ($[a_{1}:\cdots :a_{n+1}] \mapsto [\overline{-a_{2}}:\overline{a_{1}}: ... : \overline{-a_{n+1}}:\overline{a_{n}}]$). This will also give fixed point free self homeomorphisms of many products (i.e, if any of the summands are odd complex dimension), so I don't see immediately how LFPT could be applied here. | |
| Nov 19, 2018 at 16:26 | comment | added | Will Sawin | Doesn’t this follow quickly from the Lefschetz fixed point formula? | |
| Nov 19, 2018 at 16:06 | comment | added | YCor | Related (case $k=1$) mathoverflow.net/questions/315449 | |
| Nov 19, 2018 at 14:28 | comment | added | Shivani Sengupta | @YCor Yes $p$ is a prime. | |
| Nov 19, 2018 at 14:27 | history | edited | Shivani Sengupta | CC BY-SA 4.0 |
added 6 characters in body
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| Nov 19, 2018 at 14:26 | comment | added | YCor | Do you assume $p$ prime (it matters if $p=4$) | |
| Nov 19, 2018 at 14:26 | history | edited | YCor | CC BY-SA 4.0 |
clarified the question
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| Nov 19, 2018 at 14:23 | history | asked | Shivani Sengupta | CC BY-SA 4.0 |