Quasi-states and symplectic intersections

TL;DR

This paper connects symplectic topology with quasi-states from functional analysis, using Floer theory to derive new intersection rigidity results in symplectic manifolds.

Contribution

It introduces a novel link between symplectic topology and quasi-states, leveraging spectral invariants to prove intersection rigidity results.

Findings

Established a connection between quasi-states and Floer theory.

Proved new results on symplectic intersection rigidity.

Linked algebraic structures to geometric properties in symplectic manifolds.

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.