Timeline for subset embedding gives trefoil knot [closed]
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2014 at 4:51 | history | closed |
Ryan Budney Misha Steven Sam S. Carnahan♦ |
Not suitable for this site | |
| May 19, 2014 at 21:25 | review | Close votes | |||
| May 20, 2014 at 7:07 | |||||
| Jul 16, 2011 at 20:06 | comment | added | algori | .. unless they are revising for a resit. Anyway, we'll probably never know. | |
| Jul 16, 2011 at 20:03 | comment | added | algori | Ryan -- what I meant was: one can not be sure that this is homework until one has found a homework style solution. The solution that uses the classification of Seifert fibered spaces may or may not be such a solution, depending on what was covered in the course. So until further evidence is revealed I'm prepared to give the author the benefit of doubt. Besides, this time of year is not when people usually ask for help with homework solutions. | |
| Jul 16, 2011 at 17:44 | comment | added | Ryan Budney | I'm not sure what you're getting at regarding the innocent/guilty comment. Whether you use the classification or just the idea behind the classification in this one case (i.e. orbit decomposition of a space), it's no major difference and quickly leads you to the answer. Either way this isn't a research-level question. A Google search on "finite subset spaces" gives many relevant references including proofs of the requested statement. | |
| Jul 16, 2011 at 16:49 | comment | added | algori | Ryan -- innocent until proven guilty, no? And I think using the classification of Seifert fibered spaces to solve this is a bit of an overkill. | |
| Jul 16, 2011 at 15:59 | comment | added | Ryan Budney | I think it would be best to post your question on math.stackexchange.com. Also, it might be a good idea to give people more background on your motivation for this question. | |
| Jul 16, 2011 at 15:58 | comment | added | algori | student -- I've put back ticks around the formula with brackets. | |
| Jul 16, 2011 at 15:57 | history | edited | algori | CC BY-SA 3.0 |
backticks added
|
| Jul 16, 2011 at 15:56 | comment | added | Ryan Budney | Is this a homework problem? Depending on what you know there's various efficient proofs. One way is to notice $E_3(S^1)$ is 3-dimensional, and it has an action of $SO_2$ since $S^1$ does. This makes it a Seifert Fibred Space, and these were classified by Seifert. So you need only identify the quotient space and classify the singular fibres, in this case there's one with isotropy of order 2, and one with isotropy of order 3. A trefoil is a (2,3)-torus knot. | |
| Jul 16, 2011 at 15:34 | history | asked | student | CC BY-SA 3.0 |