The Burau matrix and Fiedler's invariant for a closed braid (Q1304878)

\textit{T. Fiedler} introduced an invariant for a knot in a line bundle over a surface [Topology 32, No. 2, 281-294 (1993; Zbl 0787.57007)]. In the special case of a braid regarded as a knot in a solid torus the author shows that Fiedler's invariant can be calculated from the 2-variable Alexander polynomial of the link consisting of the closed braid and its axis. The proof uses Burau's representation of the braid group. The author suggests to look at the generalized situation of an arbitrary 2-component link and its 2-variable Alexander polynomial and extracts from it a Fiedler-type invariant for one component in the complement of the second.