Geodesic
A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2027-2041

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In this paper we show that given any 3-manifold N and any non-fibered class in H1(N;Z) there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.
DOI : 10.4171/jems/412
Classification : 57-XX
Keywords: twisted Alexander polynomials, fibered 3-manifolds, symplectic 4-manifolds 
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     author = {Stefan Friedl and Stefano Vidussi},
     title = {A vanishing theorem for twisted {Alexander} polynomials with applications to symplectic 4-manifolds},
     journal = {Journal of the European Mathematical Society},
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     doi = {10.4171/jems/412},
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Stefan Friedl; Stefano Vidussi. A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2027-2041. doi: 10.4171/jems/412

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