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I got a homework asking me to show the fundamental group of the complement of the Borromean rings (say, $S^3\setminus B$ where $B$ is the Borromean rings) I know there should be three generators, but I had a hard time to find the relations; I know In the case of two unlinked circles, the commutator is 1;

enter image description hereThank you very much for the help!

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I remember Hatcher has wrote a algebraic topology, the first chapter of that book has the result.. – lee Dec 5 '12 at 8:36
it says that circle C links with circle A,B in a way as $aba^{-1}b^{-1}$, but I want to show that $[a,[b,c^{-1}]]=1$ – John0417 Dec 5 '12 at 8:45
I think I got it, using Wirtinger Presentation and get 6 relations, then reduce them to 3 as the form of commutators – John0417 Dec 5 '12 at 17:43
I skip the exercise about Wirtinger... Maybe you should write the answer down. – lee Dec 6 '12 at 5:27
Would you mind sharing your answer? – draks ... May 21 '13 at 20:41

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