Volume 18, issue 1 (2018)

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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

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.

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symplectomorphism group, simplicial manifold, characteristic class
Mathematical Subject Classification 2010
Primary: 57R17, 57R50
Secondary: 55R40, 58H10
Received: 26 May 2016
Revised: 22 February 2017
Accepted: 5 June 2017
Published: 10 January 2018
Ryoji Kasagawa
Department of Mathematics
College of Science and Technology
Nihon University