Lagrangian configurations and Hamiltonian maps

Lagrangian configurations and Hamiltonian maps

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 o...

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Veröffentlicht in:Compositio mathematica 2023-12, Vol.159 (12), p.2483-2520
Hauptverfasser: Polterovich, Leonid, Shelukhin, Egor
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Sprache:eng
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Configurations
Geometry
Hamiltonian functions
Manifolds (mathematics)
Subgroups
Topology
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creator Polterovich, Leonid
Shelukhin, Egor
description 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.
doi_str_mv 10.1112/S0010437X23007455
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1570-5846
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source Cambridge University Press Journals Complete
subjects Configurations
Geometry
Hamiltonian functions
Manifolds (mathematics)
Subgroups
Topology
title Lagrangian configurations and Hamiltonian maps
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