玻尔-索默菲尔德剖面手术和磁盘电位

arXiv - MATH - Symplectic Geometry Pub Date : 2024-09-17 DOI:arxiv-2409.11603

Soham Chanda

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引用次数: 0

摘要

我们通过在两个精确填充的拉格朗日之间切换，构建了一种新的外科手术，我们称之为 BSP 手术。在某些情况下，这种手术可以保持拉格朗日的单调性。我们证明了在玻尔-索默费尔德配置下，盘势在手术中变化的穿墙类型公式。作为应用，我们证明了比兰的圆捆绑提升可以接受玻尔-索默费尔德类型的手术。我们利用关于盘势的壁交定理来构造 $\bP^n$ 中的奇异单调拉格朗日转矩。

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Bohr-Sommerfeld profile surgeries and Disk Potentials

We construct a new surgery type operation by switching between two exact fillings of Legendrians which we call a BSP surgery. In certain cases, this surgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type formula for the change of the disk-potential under surgery with Bohr-Sommerfeld profiles. As an application, we show that Biran's circle-bundle lifts admit a Bohr-Sommerfeld type surgery. We use the wall-crossing theorem about disk-potentials to construct exotic monotone Lagrangian tori in $\bP^n$.

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arXiv - MATH - Symplectic Geometry

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