Timeline for Subsets of $\mathbb{S}^n$ fixed by an orientation-reversing self-homeomorphism — Part 2
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 29, 2022 at 9:49 | history | edited | YCor | CC BY-SA 4.0 |
fixed --
|
| Aug 29, 2022 at 5:00 | answer | added | Shijie Gu | timeline score: 1 | |
| Aug 28, 2022 at 7:15 | comment | added | Shijie Gu | I think there is an ambiently-reversible wild Canter set. Recall that R. H. Bing was the first to produce exotic involution of S^3 having wild fixed points. In particular, he showed that AH $\cup_{id}$ AH is homeomorphic to S^3, where AH denotes the crumpled 3-cube bounded by the Alexander horned sphere. One may have more examples by requiring that the crumpled cubes satisfy the Disjoint Disk Property. | |
| Aug 23, 2022 at 8:57 | comment | added | Agelos | BTW, one can ask which subsets of $\mathbb{S}^n$ are setwise reversible, but I don't expect the answer to be nice. | |
| Aug 23, 2022 at 8:53 | comment | added | YCor | Ah, indeed, I didn't notice "pointwise" | |
| Aug 23, 2022 at 8:52 | history | edited | YCor | CC BY-SA 4.0 |
fixed title
|
| Aug 23, 2022 at 8:47 | comment | added | Agelos | @YCor: we want to fix $Z$ pointwise, so I don't see how your example is reversible. | |
| Aug 23, 2022 at 8:43 | history | edited | Agelos | CC BY-SA 4.0 |
added 1 character in body
|
| Aug 22, 2022 at 21:19 | comment | added | YCor | To produce a reversible one is quite trivial. Just take $K$ wild Cantor with $K\cap -K$ empty, and consider $K\cup -K$. | |
| Aug 22, 2022 at 20:18 | history | asked | Agelos | CC BY-SA 4.0 |