使用$ECH = SWF$的拉格朗日环面不变量

Pub Date : 2019-10-08 DOI:10.4310/jsg.2021.v19.n4.a3

Chris Gerig

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引用次数: 0

摘要

我们构造了与辛4流形及其同位素类中的拉格朗日环面相关的3环面的嵌入接触同调(和单极子花同调)中的区分元素。它们不是新的不变量，而是重新包装了各种环体手术的Gromov(和Seiberg-Witten)不变量。然后，我们恢复了沿3环面Seiberg-Witten不变量乘积公式的Morgan-Mrowka-Szabo结果。

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Lagrangian torus invariants using $ECH = SWF$

We construct distinguished elements in the embedded contact homology (and monopole Floer homology) of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes. They turn out not to be new invariants, instead they repackage the Gromov (and Seiberg-Witten) invariants of various torus surgeries. We then recover a result of Morgan-Mrowka-Szabo on product formulas for the Seiberg-Witten invariants along 3-tori.

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