We'll discuss a conjecture of Dunfield-Friedl-Jackson that implies
that the twisted Alexander polynomial of a hyperbolic knot detects the
genus, twisted by the discrete faithful representation into SL_2(C). We
explain a reduction to sutured manifolds which are twisted homology
products, and prove this for a class of knots which include knots with
trivial Alexander polynomial. This is joint work with Nathan Dunfield.