@article{1dacd2a5e9bd41a387a87f9730b55399,
title = "Lagrangian configurations and Hamiltonian maps",
abstract = "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 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.",
keywords = "Floer theory, Hamiltonian diffeomorphism, Hofer's metric, Lagrangian submanifold, Poincar{\'e} recurrence, orbifold, symmetric product, symplectic manifold",
author = "Leonid Polterovich and Egor Shelukhin",
note = "Publisher Copyright: {\textcopyright} 2023 The Author(s).",
year = "2023",
month = sep,
day = "18",
doi = "10.1112/S0010437X23007455",
language = "אנגלית",
volume = "159",
pages = "2483--2520",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "12",
}