JournalsjemsVol. 15, No. 6pp. 2027–2041

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

  • Stefano Vidussi

    University of California, Riverside, United States
  • Stefan Friedl

    Universität Regensburg, Germany
A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds cover
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Abstract

In this paper we show that given any 3-manifold NN and any non-fibered class in H1(N;Z)H^1(N;\mathbb 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 33-manifold groups. This result allows us to completely classify symplectic 44-manifolds with a free circle action, and to determine their symplectic cones.

Cite this article

Stefano Vidussi, Stefan Friedl, A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds. J. Eur. Math. Soc. 15 (2013), no. 6, pp. 2027–2041

DOI 10.4171/JEMS/412