Quasi-morphisms and Symplectic Quasi-states for Convex Symplectic Manifolds

2011/10/31 by Sergei Lanzat · 22 citations
Mathematics · #Floer homology #Geometric and Algebraic Topology #Geometry and complex manifolds #Hamiltonian (control theory) #Mathematical Dynamics and Fractals #Mathematics #Morphism #Pure mathematics #Symplectic geometry #Symplectic manifold #Symplectic matrix #Symplectic representation #Symplectic vector space #Symplectomorphism #math.SG #msc:53D05 #msc:53D40 #msc:53D45

paper · pdf · doi:10.1093/imrn/rns205

published in International Mathematics Research Notices 2013(23), 5321-5365 (Oxford University Press) · 38 pages;v2: introduction rewritten, section 3.6 concerning open manifolds added, several typos corrected

arxiv created 2011/12/21 · openalex publication_date 2012/09/05 · arxiv updated 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of nonclosed strongly semi-positive symplectic manifolds (M,ω). This leads to a construction of (partial) symplectic quasi-states on the space Ccc(M) of continuous functions on M that are constant near infinity. The work extends the results by Entov and Polterovich which apply in the closed case.

Citations

• Quasi-morphisms on cotangent bundles and symplectic homogenization
• Floer homology and Novikov rings
• Quantum Structures for Lagrangian Submanifolds
• C⁰-rigidity of Poisson brackets
• Calabi quasimorphism and quantum homology
• Symplectic manifolds with contact type boundaries
• Calabi quasi-morphisms for some non-monotone symplectic manifolds

Cited by

• Hamiltonian Floer homology for compact convex symplectic manifolds