A cocycle on the group of symplectic diffeomorphisms

Jarek Kedra, Swiatoslaw Gal

Research output: Contribution to journalArticle

2 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 languageEnglish
Pages (from-to)73-88
Number of pages16
JournalAdvances in Geometry
Volume11
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011

Fingerprint

Cocycle
Diffeomorphisms
Symplectic Manifold
Finitely Generated Group
Discrete Group
Subgroup
Alternatives
Theorem

Keywords

  • symplectic manifold
  • group action
  • discrete group

Cite this

A cocycle on the group of symplectic diffeomorphisms. / Kedra, Jarek; Gal, Swiatoslaw.

In: Advances in Geometry, Vol. 11, No. 1, 01.01.2011, p. 73-88.

Research output: Contribution to journalArticle

Kedra, Jarek ; Gal, Swiatoslaw. / A cocycle on the group of symplectic diffeomorphisms. In: Advances in Geometry. 2011 ; Vol. 11, No. 1. pp. 73-88.
@article{412aae153a8b4f5388adf94869900e01,
title = "A cocycle on the group of symplectic diffeomorphisms",
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.",
keywords = "symplectic manifold, group action, discrete group",
author = "Jarek Kedra and Swiatoslaw Gal",
year = "2011",
month = "1",
day = "1",
doi = "10.1515/ADVGEOM.2010.039",
language = "English",
volume = "11",
pages = "73--88",
journal = "Advances in Geometry",
issn = "1615-715X",
publisher = "Walter de Gruyter GmbH",
number = "1",

}

TY - JOUR

T1 - A cocycle on the group of symplectic diffeomorphisms

AU - Kedra, Jarek

AU - Gal, Swiatoslaw

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

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.

KW - symplectic manifold

KW - group action

KW - discrete group

U2 - 10.1515/ADVGEOM.2010.039

DO - 10.1515/ADVGEOM.2010.039

M3 - Article

VL - 11

SP - 73

EP - 88

JO - Advances in Geometry

JF - Advances in Geometry

SN - 1615-715X

IS - 1

ER -