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Quasi-states and symplectic intersections

Michael Entov·Leonid Polterovich
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Abstract

We establish a link between symplectic topology and a recently emerged branch of functional analysis called the theory of quasi-states and quasi-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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Michael Entov, Leonid Polterovich. 2005-05-19. Quasi-states and symplectic intersections. https://arxiv.org/abs/math/0410338

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