
arXiv: 2306.03888
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.
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
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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