Quasi-states and symplectic intersections

Details Quasi-states and symplectic intersections Quasi-states and symplectic intersections

2004-10-14

arxiv.org/abs/math/0410338v2

Mathematics

Symplectic Geometry

Updated, a new section on history and physical meaning of quasi-states added. To appear in Comment. Math. Helv

Scientific paper

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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