2015/10/31 by Yi Ni
Mathematics · #Algebraic Geometry and Number Theory #Fiber bundle #Fibered knot #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot complement #Knot theory #Symplectic geometry #Torus #math.GT #math.SG #msc:57M10 #msc:57M50 #msc:57R17
paper · pdf · doi:10.1112/topo.12002
v2: incorporates referee's comments, to appear in Journal of Topology
openalex created_date 2016/06/24 · arxiv created 2016/11/11 · openalex publication_date 2017/01/01 · arxiv updated 2017/05/17 · openalex updated_date 2026/08/06
Suppose that X is a torus bundle over a closed surface with homologically essential fibers. Let X K be the manifold obtained by Fintushel–Stern knot surgery on a fiber using a knot K ⊂ S 3 . We prove that X K has a symplectic structure if and only if K is a fibered knot. The proof uses Seiberg–Witten theory and a result of Friedl–Vidussi on twisted Alexander polynomials.