Rigid subsets of symplectic manifolds

Michael Entov, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

91 Scopus citations


We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the works of P. Albers and P. Biran-O. Cornea) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.

Original languageEnglish
Pages (from-to)773-826
Number of pages54
JournalCompositio Mathematica
Issue number3
StatePublished - May 2009


  • Floer homology
  • quantum homology
  • quasi-state
  • rigidity of intersections
  • sympletic manifold

ASJC Scopus subject areas

  • Algebra and Number Theory


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