Timeline for Commutativity in the Fundamental Group and Knot Theory
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2013 at 13:51 | answer | added | Misha | timeline score: 3 | |
| Sep 7, 2013 at 12:05 | answer | added | Neil Hoffman | timeline score: 2 | |
| Sep 6, 2013 at 7:49 | comment | added | Misha | The question still makes no sense to me: Every element of $\pi_1(M,x)$ is represented by infinitely many (isotopy classes of) knots. It is even worse for a pair of knots with the common base-point. Lastly, you have to deal with non-uniqueness of resolution of the crossing of $\alpha$ and $\beta$. I suggest you think more about the question you are trying to ask. | |
| Sep 6, 2013 at 5:27 | history | edited | Zuriel |
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| Sep 6, 2013 at 5:08 | comment | added | Zuriel | You are right. I want to look at the link $a\bigcup b$ and as $a$ and $b$ necessarliy intersect at the base point, we can actually have two ways to create the link $a\bigcup b$ if we shift $b$, say, a little bit from the basepoint so that $a$ and $b$ do not intersect. Or perhaps it is better to simply consider $a\bigcup b$ as a virtual knot? | |
| Sep 6, 2013 at 4:59 | comment | added | Fernando Muro | I find strange that you can take them to be disjoint since in order to talk about the fundamental group you have to choose a base point where every path starts and ends. | |
| Sep 6, 2013 at 4:51 | history | asked | Zuriel | CC BY-SA 3.0 |