2007/04/30 by Michael Entov, Leonid Polterovich
Mathematics · #math.SG #msc:53D40 #msc:53D12 #msc:53D20
paper · pdf · doi:10.1112/s0010437x0900400x
Significant corrections and changes in the part on monotone Lagrangian submanifolds; a comment on the relation between Futaki invariant and mixed action-Maslov homomorphism added
arxiv created 2008/10/26 · arxiv updated 2014/01/14
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.