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arXiv · 1510.07715

Fintushel--Stern knot surgery in torus bundles

Yi Ni
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Abstract

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 $K\subset S^3$. 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.

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Yi Ni. 2016-11-11. Fintushel--Stern knot surgery in torus bundles. https://doi.org/10.1112/topo.12002

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