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

By Stefan Friedl, Stefano Vidussi. 2012

51 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77ea6811c4beb32120cfd4c73da3a97b932d6ee2