Rigid subsets of symplectic manifolds

95Citations
Citations of this article
14Readers
Mendeley users who have this article in their library.

Abstract

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. Copyright © Foundation Compositio Mathematica 2009.

Cite

CITATION STYLE

APA

Entov, M., & Polterovich, L. (2009). Rigid subsets of symplectic manifolds. Compositio Mathematica, 145(3), 773–826. https://doi.org/10.1112/S0010437X0900400X

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free