The symmetric commutator homology of link towers and homotopy groups of 3-manifolds (Q902286)

A link tower in a 3-manifold \(M\) is a sequence \(\{L_i\}\) of links such that each \(L_n\) is obtained from \(L_{n+1}\) by removing the last component. The authors assign a chain complex of non-abelian groups to the link tower, where the \(n\)-th group is obtained from \(\pi_1(M \setminus L_n)\) using an iterated commutator subgroup. The authors prove that, for a strongly non-splittable link tower, the \(n\)th homology group of the chain complex is isomorphic to the homotopy group \(\pi_n(M)\) provided \(n\geq 2\). Furthermore, the authors note a connection of link towers with Milnor's homotopy link groups.