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2021•International Journal of MathematicsOpen access

Lagrangian submanifolds from tropical hypersurfaces

Diego Matessi

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Abstract

We prove that a smooth tropical hypersurface in [Formula: see text] can be lifted to a smooth embedded Lagrangian submanifold in [Formula: see text]. 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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What this paper is about

We prove that a smooth tropical hypersurface in [Formula: see text] can be lifted to a smooth embedded Lagrangian submanifold in [Formula: see text]. 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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Available abstract

We prove that a smooth tropical hypersurface in [Formula: see text] can be lifted to a smooth embedded Lagrangian submanifold in [Formula: see text]. 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.

Key concepts: Submanifold, Hypersurface, Lagrangian, Mathematics, Pure mathematics, Subtropics, Biology, Ecology

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