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Is there any clear algorithm to compute the fundamental group of complements of knots?

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What do you mean by "compute"? There is the Wirtinger presentation (en.wikipedia.org/wiki/Wirtinger_presentation) but it is unclear what information you can extract from it in general. –  Qiaochu Yuan Aug 12 '12 at 2:57
    
There's also an algorithm to construct a triangulation of the complement, from which there's a standard $\pi_1$ presentation construction. –  Ryan Budney Aug 12 '12 at 5:39
    
the Wirtinger presentation was what I was looking for... Thanks guys –  Sam Aug 13 '12 at 20:01
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