Twisted Alexander polynomials detect fibered 3-manifolds

Understand

A classical result in knot theory says that the Alexander polynomial of a fibered knot is monic and that its degree equals twice the genus of the knot.

• This result has been generalized by various authors to twisted Alexander polynomials and fibered 3-manifolds.
• In this paper we show that the conditions on twisted Alexander polynomials are not only necessary but also sufficient for a 3-manifold to be fibered.
• By previous work of the authors this result implies that if a manifold of the form S^1 x N^3 admits a symplectic structure, then N fibers over S^1.