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1 I know that $H_1$ of the complement of a knot or a link can be obtained by taking the commutative quotient group which can be computed by Wirtinger presentation theorem. My questions are following I have shown that for a knot, the first homology group is the infinitely cyclic group, is this also true for a link? When I consider the higher homology groups, I tried to calculate them by M-V sequence, but it seems not work, so I wonder if there are some ways to compute them. Thanks advanced! algebraic-topology homology-cohomology share | cite | improve this question edited Nov 27 at 1:09 Kyle Miller