  We introduce a new algebraic topological technique to detect non-fibred knots
in the three sphere using the twisted Alexander invariants. As an application,
we show that for any Seifert matrix of a knot with a nontrivial Alexander
polynomial, there exist infinitely many non-fibered knots with the given
Seifert matrix. We illustrate examples of knots that have trivial Alexander
polynomials but do not have twisted Alexander invariants of fibred knots.
