A cocycle on the group of symplectic diffeomorphisms

Jarek Kedra; Swiatoslaw Gal

doi:10.1515/ADVGEOM.2010.039

A cocycle on the group of symplectic diffeomorphisms

Jarek Kedra, Swiatoslaw Gal

Mathematical Science

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	73-88
Number of pages	16
Journal	Advances in Geometry
Volume	11
Issue number	1
DOIs	https://doi.org/10.1515/ADVGEOM.2010.039
Publication status	Published - 1 Jan 2011

Keywords

symplectic manifold
group action
discrete group

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http://arxiv.org/abs/0807.1191

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AB - 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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JO - Advances in Geometry

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A cocycle on the group of symplectic diffeomorphisms

Abstract

Keywords

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