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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 11, Issue 1 (Jan 2011)


A cocycle on the group of symplectic diffeomorphisms

Światosław R. Gal
  • Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, Wrocław, Poland
  • Email:
/ Jarek Kędra
  • Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen AB243UE, Scotland, UK
  • Institute of Mathematics, University of Szczecin, ul.Wielkopolska 15, 70-451 Szczecin, Poland
  • Email:
Published Online: 2011-01-07 | DOI: https://doi.org/10.1515/advgeom.2010.039


We define a cocycle on the group of Hamiltonian diffeomorphisms of a symplectically aspherical manifold and investigate its properties. The main application is an alternative proof of the Polterovich theorem about the distortion of cyclic subgroups in finitely generated groups of Hamiltonian diffeomorphisms.

Key words.: Symplectic manifold; group action; discrete group

About the article

Received: 2008-10-20

Published Online: 2011-01-07

Published in Print: 2011-01-01

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.039.

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