The Dixmier-Douady class, the action homomorphism, and group cocycles on the symplectomorphism group

DOI10.1007/s00209-024-03429-4arXiv2009.01022OpenAlexW4391269841MaRDI QIDQ6117961

Shuhei Maruyama

Publication date: 23 February 2024

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.01022

zbMATH Keywords

group cohomologycharacteristic classsymplectomorphism groupHamiltonian diffeomorphism group

Mathematics Subject Classification ID

Geometric quantization (53D50) Canonical transformations in symplectic and contact geometry (53D22)

Cites Work

• A two-cocycle on the group of symplectic diffeomorphisms
• On distortion in groups of homeomorphisms
• On the homology of Lie groups made discrete
• Cohomology of symplectomorphism groups and critical values of Hamiltonians
• Principal bundles and the Dixmier Douady class
• The flux homomorphism and central extensions of diffeomorphism groups
• \(K\)-theoretic invariants of Hamiltonian fibrations
• The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures
• The Calabi invariant and the Euler class
• An Introduction to Contact Topology
• Quantization and unitary representations
• Cohomology of Group Extensions
• Loop spaces, characteristic classes and geometric quantization
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