Timeline for Oriention-Reversing Diffeomorphisms of a Manifold
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2010 at 16:46 | comment | added | Randall | I accidentally wrote "orientational" instead of orientation in the title, so I apologize for that. I'm not sure how you deduce from that and that I used the common abbreviation $\mathbb{P}^n$ for complex projective space that I had no idea what I was talking about / that this is a homework question. As I said, I'm not a topologist and since every complex manifold is orientable it seemed natural to ask when you can reverse the orientation. I know we don't want to answer calculus questions here but it seems rather silly that I can't ask questions outside my area of specialty. | |
| Apr 22, 2010 at 14:55 | comment | added | Charlie Frohman | When this question first appeared, there was some approximation of orientation reversing in the title, and the person asking the question, with what is clearly an alias as a name, didn't seem to know the question was about complex projective spaces. Mariano edited it to be coherent, after Allen Knutson gave a coherent answer to it. Finally, I ask this as a homework question whenever I teach cup products. The only Randy Reddick who shows up in google searches is a journalist. | |
| Apr 20, 2010 at 19:28 | answer | added | John Francis | timeline score: 18 | |
| Apr 19, 2010 at 17:56 | comment | added | Makhalan Duff | Can you down-vote a comment? | |
| Apr 19, 2010 at 6:23 | answer | added | HenrikRüping | timeline score: 2 | |
| Apr 19, 2010 at 5:20 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
edited title
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| Apr 19, 2010 at 2:54 | answer | added | Jason DeVito - on hiatus | timeline score: 14 | |
| Apr 19, 2010 at 2:30 | vote | accept | Randall | ||
| Apr 19, 2010 at 1:06 | answer | added | Allen Knutson | timeline score: 18 | |
| Apr 19, 2010 at 0:15 | comment | added | Ryan Budney | I doubt you'll get any simultaneously conceptually appealing, compact and non-vacuous answers to your question. Your orientation-reversing map may not be of finite-order. It may or may not have fixed points. Consider the case of knot complements in $S^3$ for example. Admitting an orientation-reversing diffeomorphism amounts to saying the knot is amphicheiral. There are if and only if type statements for such manifolds but they're not exactly simple or fully informative. | |
| Apr 18, 2010 at 22:45 | comment | added | Randall | Yes I mean $\mathbb{C}\mathbb{P}^{2n}$. Sorry if this question is actually easy, but I am not a differential geometer so I'm unsure of how to approach this. I checked google and noticed a few theses on when manifolds admit such a morphism so I assumed it wasn't completely trivial. | |
| Apr 18, 2010 at 22:37 | comment | added | S. Carnahan♦ | When you say $\mathbb{P}^{2n}$, do you mean complex projective space? I think real projective spaces of even dimension are very rarely orientable. | |
| Apr 18, 2010 at 22:09 | comment | added | Charlie Frohman | Dude, If you turn in any answers you get off of here as your solution to a homework problem, I am totally turning you in. | |
| Apr 18, 2010 at 22:06 | history | asked | Randall | CC BY-SA 2.5 |