Distinguishing algebraic models for the open symplectic mapping tori

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• Baris Kartal, MIT
• Wednesday 24 October 2018, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Mark Gross.

One can construct \textbf{the open symplectic mapping torus} $T_\phi$ for a given Weinstein manifold $M$ and a compactly supported exact symplectomorphism $\phi$. $T_\phi$ is another Weinstein manifold, and its contact boundary is independent of $\phi$. In this talk, we will show how to distinguish $T_\phi$ from $T_{1_M}$. We first construct an algebraic model- \textbf{the mapping torus category}- for the (wrapped) Fukaya category of $T_\phi$. The construction is inspired by mirror symmetry for the punctured torus, and it involves the geometry of the Tate curve. Then we will exploit dynamics and deformation theory of these algebraic models to show they are not equivalent categories.

This talk is part of the Algebraic Geometry Seminar series.

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