Non-isotopic monotone Lagrangian submanifolds of $\mathbb{C}^n$
Symplectic Geometry
2020-03-03 v2
Abstract
Let be a Delzant polytope in with facets. We associate a closed Lagrangian submanifold of to each Delzant polytope. We prove that is monotone if and only if and only if the polytope is Fano. We pose the "Lagrangian version of Delzant Theorem". Then for even and we construct monotone Lagrangian embeddings of into , no two of which are related by Hamiltonian isotopies. Some of these embeddings are smoothly isotopic and have equal minimal Maslov numbers, but they are not Hamiltonian isotopic. Also, we construct infinitely many non-monotone Lagrangian embeddings of into , no two of which are related by Hamiltonian isotopies.
Keywords
Cite
@article{arxiv.1911.11407,
title = {Non-isotopic monotone Lagrangian submanifolds of $\mathbb{C}^n$},
author = {Vardan Oganesyan},
journal= {arXiv preprint arXiv:1911.11407},
year = {2020}
}
Comments
This paper has been withdrawn by the author because of the error in the proof