On a quasimorphism of Hamiltonian diffeomorphisms and quantization

In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology: the Calabi-Weinstein morphism and a quasimorphism on the universal cover of the Hamiltonian diffeomorphism group introduced by Entov, Py, Shelukhin.

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Received 8 November 2019

Received revised 17 March 2023

Accepted 5 April 2023

Published 4 June 2024