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.

arXiv commentMinor corrections

References in corpus (15)

• Rigidity and uniruling for Lagrangian submanifolds
• Spectral numbers in Floer theories
• Commuting Hamiltonians and multi-time Hamilton-Jacobi equations
• Making Almost Commuting Matrices Commute
• Calabi quasi-morphisms for some non-monotone symplectic manifolds
• Microlocal condition for non-displaceablility
• Symplectic geometry of quantum noise
• Quasi-morphisms on contactomorphism groups and contact rigidity
• C^0-rigidity of Poisson brackets
• Symplectic quasi-states on the quadric surface and Lagrangian submanifolds
• Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds
• Descent and C^0-rigidity of spectral invariants on monotone symplectic manifolds
• An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics
• Unboundedness of the Lagrangian Hofer distance in the Euclidean ball
• Compactly supported Hamiltonian loops with non zero Calabi invariant

Cited by in corpus (7)

• Bounds on spectral norms and barcodes
• Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces
• $\hat{G}$-invariant quasimorphisms and symplectic geometry of surfaces
• Quasi-state Rigidity for Finite-dimensional Lie Algebras
• Rigid fibers of spinning tops
• Disjoint superheavy subsets and fragmentation norms
• A class of new bi-invariant metrics on the Hamiltonian diffeomorphism groups