The knot group (the fundamental group of the complement of a knot) of the unknot is $\mathbb{Z}$ and the Hopf link is $\mathbb{Z}^2$, so those are knots (links) with Abelian knot group but are there any more?
What knot groups are Abelian?
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general-topology
low-dimensional-topology
knot-theory
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1At least for a knot, what would that say about the Wirtinger representation of the knot group? – 2012-03-19