Calabi quasimorphism and quantum homology
Symplectic Geometry
2007-05-23 v2 Differential Geometry
Dynamical Systems
Abstract
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.
Cite
@article{arxiv.math/0205247,
title = {Calabi quasimorphism and quantum homology},
author = {Michael Entov and Leonid Polterovich},
journal= {arXiv preprint arXiv:math/0205247},
year = {2007}
}
Comments
Revised and considerably extended version; links to Seidel representation and combinatorics added