JournalscmhVol. 81 , No. 1DOI 10.4171/cmh/43

Quasi-states and symplectic intersections

  • Leonid Polterovich

    Tel-Aviv University, Israel
  • Michael Entov

    Technion - Israel Institute of Technology, Haifa, Israel
Quasi-states and symplectic intersections cover


We establish a link between symplectic topology and a recently emerg\-ed branch of functional analysis called the theory of quasi-states and quasi-measures (also known as topological measures). In the symplectic context quasi-states can be viewed as an algebraic way of packaging certain information contained in Floer theory, and in particular in spectral invariants of Hamiltonian diffeomorphisms introduced recently by Yong-Geun Oh. As a consequence we prove a number of new results on rigidity of intersections in symplectic manifolds. This work is a part of a joint project with Paul Biran.