Hofer-continuous quasi-morphisms on Liouville manifolds

2025/09/27 by Zapolsky, Frol
#46J10 #53D99 #FOS: Mathematics #Functional Analysis (math.FA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2509.23277

Abstract

We show that, given a complete Liouville manifold, any homogeneous quasi-morphism on its Hamiltonian group, which satisfies a strengthened version of Hofer continuity called stability, must vanish. This partially addresses a conjecture due to L. Polterovich.

Citations

• Viterbo conjecture for Zoll symmetric spaces
• Calabi quasimorphisms for monotone coadjoint orbits
• Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization
• The Action homomorphism, quasimorphisms and moment maps on the space of\n compatible almost complex structures
• A comparison of symplectic homogenization and Calabi quasi-states
• Symplectic quasi-states and semi-simplicity of quantum homology
• Quasi-morphisms and the Poisson bracket
• Calabi quasimorphism and quantum homology

Related

• A quasi-isometric embedding into the group of Hamiltonian\n diffeomorphisms with Hofer's metric
• Quasimorphisms on surfaces and continuity in the Hofer norm
• Homogeneous quasimorphisms, C⁰-topology and Lagrangian intersection
• Autonomous Hamiltonian flows, Hofer's geometry and persistence modules
• The group of Hamiltonian homeomorphisms and continuous Hamiltonian flows