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1 results

  • Lagrangian configurations and Hamiltonian maps

  • Leonid Polterovich, Egor Shelukhin
  • Journal:
    Compositio Mathematica / Volume 159 / Issue 12 / December 2023
    Published online by Cambridge University Press:
    18 September 2023, pp. 2483-2520
    Print publication:
    December 2023
    • Article
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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 Hofer's metric, prove constraints on Lagrangian packing, find instances of Lagrangian Poincaré 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.