Calabi quasimorphism and quantum homology

Details Calabi quasimorphism and quantum homology Calabi quasimorphism and quantum homology

2002-05-23

arxiv.org/abs/math/0205247v2

Mathematics

Symplectic Geometry

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

Scientific paper

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.

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