On Newton polytopes of Lagrangian augmentations

Abstract

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 non-orientable exact Lagrangian fillings.

arXiv comment21 pages, 7 figures. A published version of this manuscript will appear in the Bulletin of the London Mathematical Society

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Cited by in corpus (1)

• Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings