Timeline for On what kind of objects do the Galois groups act?
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 8, 2011 at 20:36 | history | edited | Adrien | CC BY-SA 3.0 |
typo
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| Jul 8, 2011 at 17:28 | vote | accept | asv | ||
| Dec 16, 2011 at 16:39 | |||||
| Jul 8, 2011 at 3:54 | vote | accept | asv | ||
| Jul 8, 2011 at 16:49 | |||||
| Jul 7, 2011 at 7:59 | vote | accept | asv | ||
| Jul 7, 2011 at 13:14 | |||||
| Jul 6, 2011 at 15:52 | comment | added | Adrien | Also you can find a description of the action on finite type invariant at the end of the book of Kassel and Turaev "Quantum groups and knot invariants" | |
| Jul 6, 2011 at 15:51 | comment | added | Adrien | Well, you can check the link above wehre somebody asked a similar question, and the nice answer of Damien. From the algebraic perspective, you can read the paper of Bar Natan "On associators and the Grothendieck-Teichmuller group". For the relation with the absolute Galois group, there are a lot of surveyx on the webpage of Leila Schneps : math.jussieu.fr/~leila/articles.html | |
| Jul 6, 2011 at 14:48 | comment | added | asv | Is there a good place to read about it? | |
| Jul 6, 2011 at 14:20 | comment | added | Adrien | Now these fundamental groups are close to braid group, which explain partially the relation with knots. But the precise role that it plays in braid theory, quantum algebra and so on really comes from the beautiful work of Drinfeld. | |
| Jul 6, 2011 at 14:19 | comment | added | Adrien | So far I know, dessin d'enfants encodes finite covering of $P^1(\mathbb{C}-0,1,\infty$, which is isomorphic to the moduli space $M_{0,4}$ of Riemann spheres whith 4 marked points. On the other hand, as explained in the first link I pointed out, the Grothendieck-Teichmuller group is the automorphism group of the "tower" of fundamental groups of the $M_{0,n}$ equipped with natural geometric operations like adding or erasing points. So they have the same origin and in both case the faithfulness follows from Belyi's theorem. | |
| Jul 6, 2011 at 14:13 | vote | accept | asv | ||
| Jul 7, 2011 at 6:12 | |||||
| Jul 6, 2011 at 13:32 | comment | added | asv | The examples of knots and quantum algebra are new for me. Are they directly related to dessins d'enfants or the construction of the action of $G_{\mathbb{Q}}$ is really different? (Even if such a relation does exist, I can imagine that by itself it should be very surprising and far from obvious.) | |
| Jul 6, 2011 at 13:10 | history | edited | Adrien | CC BY-SA 3.0 |
added 91 characters in body
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| Jul 6, 2011 at 13:04 | history | answered | Adrien | CC BY-SA 3.0 |