A second cohomology class of the symplectomorphism group with the discrete topology

Kasagawa, Ryoji

doi:10.2140/agt.2018.18.187

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A second cohomology class of the symplectomorphism group with the discrete topology

Ryoji Kasagawa

Algebraic & Geometric Topology 18 (2018) 187–219

DOI: 10.2140/agt.2018.18.187

Abstract

A second cohomology class of the group cohomology of the symplectomorphism group is defined for a symplectic manifold with first Chern class proportional to the class of symplectic form and with trivial first real cohomology. Some properties of it are studied. In particular, it is characterized in terms of cohomology classes of the universal symplectic fiber bundle over the classifying space of the symplectomorphism group with the discrete topology.

Keywords

symplectomorphism group, simplicial manifold, characteristic class

Mathematical Subject Classification 2010

Primary: 57R17, 57R50

Secondary: 55R40, 58H10

References

Publication

Received: 26 May 2016

Revised: 22 February 2017

Accepted: 5 June 2017

Published: 10 January 2018

Authors

Ryoji Kasagawa
Department of Mathematics College of Science and Technology Nihon University Surugadai Chiyoda-ku Japan

Volume 18, issue 1 (2018)