Quasi-morphisms and quasi-states in symplectic topology

Abstract

This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of Poisson brackets and algebraic and metric properties of symplectomorphism groups.

Minor corrections

References in corpus (4)

• Microlocal condition for non-displaceablility
• C^0-rigidity of Poisson brackets
• Symplectic quasi-states on the quadric surface and Lagrangian submanifolds
• An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics

Cited by in corpus (3)

• $\hat{G}$-invariant quasimorphisms and symplectic geometry of surfaces
• A class of new bi-invariant metrics on the Hamiltonian diffeomorphism groups
• Disjoint superheavy subsets and fragmentation norms