As the question title suggests, how do I see that any one Wirtinger relation is a consequence of the remainder?
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2$\begingroup$ There is nothing unclear about this question. Every crossing of a knot diagram yields one relation for the Wirtinger presentation of the knot group. It seems that one of these relations is redundant and thus can be omitted from the presentation, and the question is asking why. $\endgroup$– ThiKuCommented Oct 3, 2016 at 14:52
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$\begingroup$ If you look at the knot diagram from above and imagine a loop beneath it and circling it, then the loop is contractible in the space less the knot, but from above in this contraction the loop goes through each crossing. That is how I see it. A more formal proof is probably better using groupoids, but that is not to general taste. $\endgroup$– Ronnie BrownCommented Oct 3, 2016 at 20:41
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$\begingroup$ Why don't you write this up as an answer? $\endgroup$– ThiKuCommented Oct 4, 2016 at 1:31
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