Twisted Alexander polynomials detect fibered 3-manifolds

By Stefan Friedl, Stefano Vidussi. 2008

89 citations recorded by the source corpus.

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. In fact we will completely determine the symplectic cone of S^1 x N in terms of the fibered faces of the Thurston norm ball of N.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ee8570e961477aaee7651208931acfdca3b1a137

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In Computational Theory and Mathematics

1. Stefano Vidussi
2. Stefan Friedl

In Geometry and Topology

1. Stefano Vidussi
2. Stefan Friedl
3. Charles Livingston

In Mathematical Physics

1. Stefano Vidussi
2. Stefan Friedl
3. Charles Livingston

Citations in the corpus

• The Thurston norm and twisted Alexander polynomials (2012, methodology): “In [16] (see also [15]) the authors showed that in fact twisted Alexander polynomials detect fibered 3-manifolds.”