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A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds

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Friedl, Stefan ; Vidussi, S.
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Date of publication of this fulltext: 05 Sep 2016 10:56


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.

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