Lagrangian configurations and Hamiltonian maps

Leonid Polterovich, Egor Shelukhin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 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.

Original languageEnglish
Pages (from-to)2483-2520
Number of pages38
JournalCompositio Mathematica
Volume159
Issue number12
DOIs
StatePublished - 18 Sep 2023

Funding

FundersFunder number
Natural Sciences and Engineering Research Council of Canada
Fonds de recherche du Québec – Nature et technologies
Israel Science Foundation1102/20
Courtois Foundation

    Keywords

    • Floer theory
    • Hamiltonian diffeomorphism
    • Hofer's metric
    • Lagrangian submanifold
    • Poincaré recurrence
    • orbifold
    • symmetric product
    • symplectic manifold

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