We prove that a smooth tropical hypersurface in $mathbb R^3$ can be lifted to a smooth embedded Lagrangian submanifold in $mathbb R^3$. The idea of the proof is to use Lagrangian pairs of pants, which are the lifts of tropical hyperplanes introduced by the author in an earlier paper, as the main building blocks.
Lagrangian submanifolds from tropical hypersurfaces / D. Matessi. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 32:7(2021 May 19). [10.1142/S0129167X21500464]
Lagrangian submanifolds from tropical hypersurfaces
D. Matessi
2021
Abstract
We prove that a smooth tropical hypersurface in $mathbb R^3$ can be lifted to a smooth embedded Lagrangian submanifold in $mathbb R^3$. The idea of the proof is to use Lagrangian pairs of pants, which are the lifts of tropical hyperplanes introduced by the author in an earlier paper, as the main building blocks.
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