Twisted Alexander polynomials and fibered 3-manifolds

Details Twisted Alexander polynomials and fibered 3-manifolds Twisted Alexander polynomials and fibered 3-manifolds

2009-12-31

arxiv.org/abs/1001.0132v1

Mathematics

Geometric Topology

22pages, 2 figures to be published by the Proceedings of the Georgia International Topology Conference 2009

Scientific paper

In a series of papers the authors proved that twisted Alexander polynomials detect fibered 3-manifolds, and they showed that this implies that a closed 3-manifold N is fibered if and only if S^1 x N is symplectic. In this note we summarize some of the key ideas of the proofs. We also give new evidence to the conjecture that if $ is a symplectic 4-manifold with a free S^1-action, then the orbit space is fibered.

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