Twisted Alexander polynomials detect fibered 3-manifolds

• 成果类型: Article
• 署名作者: Friedl, Stefan; Vidussi, Stefano
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.3.8
• 发表日期: 2011
• 页码: 1587-1643
• 关键词: subgroup separability; FLOER HOMOLOGY; thurston norm; reidemeister torsion; MANIFOLDS; KNOTS; REPRESENTATIONS; INVARIANTS; COHOMOLOGY; Examples

摘要

A classical result in knot theory says that for a fibered knot the Alexander polynomial is monic and that the degree equals twice the genus of the knot. This result has been generalized by various authors to twisted Alexander polynomials and fibered 3-manifolds. In this paper we show that the conditions on twisted Alexander polynomials are not only necessary but also sufficient for a 3-manifold to be fibered. By previous work of the authors this result implies that if a manifold of the form S-1 x N-3 admits a symplectic structure, then N fibers over S-1. Infact we will completely determine the symplectic cone of S-1 x N in terms of the fibered faces of the Thurst on norm ball of N.