Alexander modules

Abstract

The Alexander modules of a link are the homology groups of the universal abelian cover of the complement of the link. For a link of n n -spheres in S n + 2 {S^{n + 2}} , we show that, if n ⩾ 2 n \geqslant 2 , the Alexander modules A 2 , … , A n {A_2}, \ldots ,{A_n} and the torsion submodule of A 1 {A_1} are all of type L L . This leads to a characterization, below the middle dimension, of the polynomial invariants of the link. These results were previously proven for the special case of boundary links.