近 Lefschetz 纤维化、Stein 结构与正则 Lagrangian 子流形
Nearly Lefschetz fibrations, Stein structures, and regular Lagrangians
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中文总结 AI 辅助
研究近Lefschetz纤维化上的Stein结构，证明四维Weinstein域中具Legendrian边界的Lagrangian圆盘均为正则，解决邻近猜想与Slice-Ribbon猜想的Lagrangian类比，并给出构造Weinstein Kirby图的算法。
中文摘要 AI 辅助
我们研究了近 Lefschetz 纤维化上的 Stein 结构，并将其应用于 Weinstein 域中的辛子流形与 Lagrangian 子流形。我们证明了，在 Weinstein 形变等价的意义下，$4$ 维 Weinstein 域中所有具有 Legendrian 边界的 Lagrangian 圆盘都是 Eliashberg-Ganatra-Lazarev 意义下的正则圆盘。这解决了二维 Lagrangian 圆盘的邻近 Lagrangian 猜想的 Weinstein 类比，并解决了 Slice-Ribbon 猜想的 Lagrangian 类比的一部分。在此过程中，我们证明了正允许近 Lefschetz 纤维化由典范 Stein 结构支撑，并在平面情形下证明了相应的拟柔性结果。这推广了 Boileau-Orevkov 的工作，该推广可能具有独立的研究兴趣。最后，我们给出了一个显式算法，从多截面补集的近 Lefschetz 纤维化结构构造 Weinstein Kirby 图。
英文摘要
We study Stein structures on nearly Lefschetz fibrations, with applications to symplectic and Lagrangian submanifolds in Weinstein domains. We prove that, up to Weinstein deformation equivalence, all Lagrangian disks with Legendrian boundary in $4$-dimensional Weinstein domains are regular in the sense of Eliashberg-Ganatra-Lazarev. This settles a Weinstein analogue of the nearby Lagrangian conjecture for two-dimensional Lagrangian disks, and resolves part of a Lagrangian analogue of the Slice-Ribbon conjecture. Along the way, we show that positive allowable nearly Lefschetz fibrations are supported by canonical Stein structures and prove a corresponding quasiflexibility result in the planar case. This yields a generalization of work of Boileau-Orevkov which may be of independent interest. Finally, we give an explicit algorithm producing a Weinstein Kirby diagram from the nearly Lefschetz fibration structure of a multisection complement.
发表机构
- University of Alabama（阿拉巴马大学）
- Boston College（波士顿学院）
- Institute for Advanced Study（高等研究院）
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