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

Stefan Friedl; Stefano Vidussi

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arXiv · 1205.2434

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

Stefan Friedl·Stefano Vidussi

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Abstract

In this paper we show that given any 3-manifold N and any non-fibered class in H^1(N;Z) there exists a representation such that the corresponding twisted Alexander polynomial is zero. This is obtained by extending earlier work of the authors, together with 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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Stefan Friedl, Stefano Vidussi. 2012-05-11. A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds. https://arxiv.org/abs/1205.2434

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