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arXiv · 2102.06118

Lagrangian configurations and Hamiltonian maps

Leonid Polterovich·Egor Shelukhin
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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.

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Leonid Polterovich, Egor Shelukhin. 2021-02-11. Lagrangian configurations and Hamiltonian maps. https://arxiv.org/abs/2102.06118

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