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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Strambach, Karl

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

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A cocycle on the group of symplectic diffeomorphisms

1Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, Wrocław, Poland

2Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen AB243UE, Scotland, UK

3Institute of Mathematics, University of Szczecin, ul.Wielkopolska 15, 70-451 Szczecin, Poland

Citation Information: Advances in Geometry. Volume 11, Issue 1, Pages 73–88, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom.2010.039, January 2011

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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

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