This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly simplifies arguments and also allows us to show that there exist Legendrian links with infinitely many nonorientable exact Lagrangian fillings.

中文翻译：

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拉格朗日增广的牛顿多面体

本文探讨了牛顿多面体在勒格朗日填充勒格朗日子流形的研究中的使用。特别是，我们表明，与里布弦的增广值相关的牛顿多面体可以区分无限多个不同的拉格朗日填充，无论是对于勒格连杆还是更高维的勒格朗日球体。我们在有限特征下进行的计算，这显着简化了论证，并且还允许我们证明存在与无限多个不可定向的精确拉格朗日填充的勒让德联系。