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Lagrangian configurations and Hamiltonian maps

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 نشر من قبل Egor Shelukhin
 تاريخ النشر 2021
  مجال البحث
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We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equipped with Hofers metric, prove constraints on Lagrangian packing, find instances of Lagrangian Poincar{e} recurrence, and present a new hierarchy of normal subgroups of area-preserving homeomorphisms of the two-sphere. The technology involves Lagrangian spectral invariants with Hamiltonian term in symmetric product orbifolds.



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