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arXiv · 1807.03420

A JSJ-type decomposition theorem for symplectic fillings

Austin Christian·Michael Menke
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Abstract

We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particular geometric condition. As an application, we show that if $(M,\xi)$ is obtained from $(S^3,\xi_{\mathrm{std}})$ via Legendrian surgery along a knot which has been stabilized both positively and negatively, then $(M,\xi)$ has a unique exact filling.

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Austin Christian, Michael Menke. 2018-07-09. A JSJ-type decomposition theorem for symplectic fillings. https://arxiv.org/abs/1807.03420

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