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https://dx.doi.org/10.48550/ar...
Article . 2023
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On Newton polytopes of Lagrangian augmentations

Authors: Orsola Capovilla‐Searle; Roger Casals;

On Newton polytopes of Lagrangian augmentations

Abstract

AbstractThis 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.

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Keywords

Lagrangian fillings, Geometric Topology (math.GT), 53D12, 57K33, 52B20, Mathematics - Geometric Topology, Lagrangian submanifolds; Maslov index, Legendrian contact dg-algebras, Mathematics - Symplectic Geometry, Symplectic aspects of Floer homology and cohomology, FOS: Mathematics, Mathematics - Combinatorics, Symplectic Geometry (math.SG), Combinatorics (math.CO), Toric varieties, Newton polyhedra, Okounkov bodies, Newton polytopes

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green