Algebraic & Geometric Topology

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

Ryoji Kasagawa

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

Permanent link to this document
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

Subjects
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]

Keywords
symplectomorphism group simplicial manifold characteristic class

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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