NDLI: Rigid subsets of symplectic manifolds

Content Provider	Scilit
Author	Entov, Michael Polterovich, Leonid
Copyright Year	2009
Description	Journal: Compositio Mathematica 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.
Ending Page	826
Starting Page	773
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x0900400x
Journal	Compositio Mathematica
Issue Number	03
Volume Number	145
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2009-05-01
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Particles and Fields Physics Symplectic Manifolds
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Rigid subsets of symplectic manifolds