2002/05/23 by Michael Entov, Entov, Michael, Leonid Polterovich +1 · 9 citations
Mathematics · #53D05 #53D22 #53D40 #53D45 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.DS #math.SG #msc:53D05 #msc:53D22 #msc:53D40 #msc:53D45
paper · pdf · doi:10.48550/arxiv.math/0205247
Revised and considerably extended version; links to Seidel representation and combinatorics added
openalex publication_date 2002/05/23 · arxiv created 2002/09/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small open subset of the sphere equals to the Calabi invariant of the diffeomorphism. This result extends to more general symplectic manifolds: If the symplectic manifold is monotone and its quantum homology algebra is semi-simple we construct a similar quasimorphism on the universal cover of the group of Hamiltonian diffeomorphisms.