Algebraic & Geometric Topology

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

Ryoji Kasagawa

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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

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

Received: 26 May 2016
Revised: 22 February 2017
Accepted: 5 June 2017
First available in Project Euclid: 1 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology 57R50: Diffeomorphisms
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]

symplectomorphism group simplicial manifold characteristic class


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.

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