We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain Kahler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated, and derive new constraints on Lagrangian tori. The key input, via homological mirror symmetry, is a result of Bayer and Bridgeland on the autoequivalence group of the derived category of an algebraic K3 surface of Picard rank one.

中文翻译：

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通过镜像对称的 $K3$ 表面的辛拓扑

我们研究了某些 K3 曲面（包括“镜面四次”和“镜面双平面”）的辛拓扑，配备了某些 Kahler 形式。特别地，我们证明辛托雷利群可以无限生成，并推导出拉格朗日环面的新约束。通过同调镜像对称，关键输入是 Bayer 和 Bridgeland 在 Picard 1 阶代数 K3 曲面的派生范畴的自等价群上的结果。