A cocycle on the group of symplectic diffeomorphisms

Details A cocycle on the group of symplectic diffeomorphisms A cocycle on the group of symplectic diffeomorphisms

2008-07-08

arxiv.org/abs/0807.1191v2

Advances in Geometry, Vol. 11, Issue 1, 2011, pp. 73-88

Mathematics

Symplectic Geometry

19 pages, no figures, corrected version

Scientific paper

10.1515/ADVGEOM.2010.039

We define a cocycle on the group of symplectic diffeomorphisms of a
symplectic manifold and investigate its properties. The main applications are
concerned with symplectic actions of discrete groups. For example, we give an
alternative proof of the Polterovich theorem about the distortion of cyclic
subgroups in finitely generated groups of Hamiltonian diffeomorphisms.

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