Poisson brackets and symplectic invariants

Lev Buhovsky, Michael Entov, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We introduce new invariants associated with collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these invariants involves various flavors of Floer theory, including the μ 3-operation in Donaldson-Fukaya category. We present applications to approximation theory on symplectic manifolds and to Hamiltonian dynamics.

Original languageEnglish
Pages (from-to)89-157
Number of pages69
JournalSelecta Mathematica, New Series
Volume18
Issue number1
DOIs
StatePublished - Mar 2012

Keywords

  • Donaldson-Fukaya category
  • Hamiltonian chord
  • Poisson brackets
  • Quasi-state
  • symplectic manifold

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy

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