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.
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Leonid Polterovich, Michael Entov, Quasi-states and symplectic intersections. Comment. Math. Helv. 81 (2006), no. 1, pp. 75–99DOI 10.4171/CMH/43