I need a reference with a proof that the inverse image of SL2(Z) in the universal covering of SL2(R) is the group of the trefoil knot (i.e. the Braid group B3 on 3 strands)
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I believe you mean the fundamental group of the complement of the trefoil knot in $\Bbb S^3$, not that of the knot itself. – Travis Willse Feb 02 '17 at 10:25
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Yes, thank you, edited. – Sirion Feb 02 '17 at 10:32
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Do you have a link to an intuitive description of $\widetilde{SL}_2(\mathbb{R})$ the universal covering space of $SL_2(\mathbb{R})$ ? – reuns Feb 02 '17 at 10:36
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No, sorry, I don't know much about covering spaces. The only thing I've found is this answer – Sirion Feb 02 '17 at 12:26
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Reference: R. Hain: Lectures on Moduli Spaces of Elliptic Curves, in Transformation Groups and Moduli Spaces of Curves, Advanced Lectures in Mathematics, edited by Lizhen Ji, S.-T. Yau no. 16 (2010), 95–166, Higher Education Press, Beijing, arXiv:0812.1803, Corollary $8.3$.
Dietrich Burde
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I'll wait a while to see if someone has a reference which does not relie on moduli spaces. Then I'll accept the answer. Thank you. – Sirion Feb 02 '17 at 10:35
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In case you would like to have another reference, we can find one. Let me know what mathematical background you have, so that it is useful for you. – Dietrich Burde Feb 02 '17 at 10:45
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I've found this statement in example 1.5.2 of the book "Trees" by Jean-Pierre Serre. The chapter it belongs is about free products with amalgamation. So any proof related with it would be great (maybe one where I can see a sort of "concrete" visualization of what's going on). Other topics I'm familiar with (which may be useful in this situation) are braid groups, coxeter groups and standard topology. – Sirion Feb 02 '17 at 12:35
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