Calabi quasimorphism and quantum homology

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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.
Revised and considerably extended version; links to Seidel representation and combinatorics added

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Symplectic Geometry, Differential Geometry, Dynamical Systems, 53D22, 53D05, 53D40, 53D45

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http://salesiana.dossiersoluciones.com/handle/123456789/64136

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205247
 http://arxiv.org/abs/math/0205247

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arXiv