2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64136We 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.Revised and considerably extended version; links to Seidel representation and combinatorics addedSymplectic GeometryDifferential GeometryDynamical Systems53D22, 53D05, 53D40, 53D45text