In this talk, we are going to obtain a presentation of the Alexander module of a 2-component link
corresponding to a pair of appropriately chosen Seifert surfaces of the components.
This presentation is due to D. Cooper and the proof to be discussed is from recent notes by
S. Melikhov (see pdf file below).
As an application of this presentation, we will compute the 2-variable Alexander polynomial of
torus links and prove two Conway Identities for the 2-variable sign-refined Alexander polynomial.
This second part of the talk is based on Cooper's dissertation (link)