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Infinitely many monotone Lagrangian tori in \(\mathbb R^6\) - MaRDI portal

Infinitely many monotone Lagrangian tori in \(\mathbb R^6\) (Q496209)

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Infinitely many monotone Lagrangian tori in \(\mathbb R^6\)
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    Infinitely many monotone Lagrangian tori in \(\mathbb R^6\) (English)
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    21 September 2015
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    The author constructs infinitely many Lagrangian tori in \(\mathbb R^6\) which are not related by Hamiltonian isotopies. He shows for every number \(n\) there is a monotone Lagrangian torus \(L \subset (\mathbb R^6 , \omega_0 )\) such that there are \(n + 2\) distinct Maslov index 2 classes in \(\pi_2 (\mathbb R^6 , L)\) for which the algebraic count of pseudo-holomorphic discs passing through a point of \(L\) is non zero. So for different \(n\) they cannot be related by symplectomorphisms. The proofs are enjoyable and easy to read.
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    Lagrangian submanifold
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    symplectomorphism
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