## Algebraic & Geometric Topology

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

Ryoji Kasagawa

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 187-219.

Dates
Revised: 22 February 2017
Accepted: 5 June 2017
First available in Project Euclid: 1 February 2018

https://projecteuclid.org/euclid.agt/1517454215

Digital Object Identifier
doi:10.2140/agt.2018.18.187

Mathematical Reviews number (MathSciNet)
MR3748242

Zentralblatt MATH identifier
1385.57027

#### Citation

Kasagawa, Ryoji. A second cohomology class of the symplectomorphism group with the discrete topology. Algebr. Geom. Topol. 18 (2018), no. 1, 187--219. doi:10.2140/agt.2018.18.187. https://projecteuclid.org/euclid.agt/1517454215

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