On contact mapping classes of prequantizations

Allout, Souheib; Sağlam, Murat

doi:10.2140/agt.2025.25.2507

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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On contact mapping classes of prequantizations

Souheib Allout and Murat Sağlam

Algebraic & Geometric Topology 25 (2025) 2507–2526

DOI: 10.2140/agt.2025.25.2507

Abstract

We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which project to the identity component of the symplectomorphism group of the base manifold. Along the way, we study the lifting problem of symplectomorphisms of the base manifold to strict contactomorphisms of the prequantization.

Keywords

prequantizations, contact mapping classes

Mathematical Subject Classification

Primary: 53D10, 53D12, 53D22

References

Publication

Received: 7 March 2024

Revised: 7 May 2024

Accepted: 26 May 2024

Published: 11 August 2025

Authors

Souheib Allout
Fakultät für Mathematik Ruhr-Universität Bochum Bochum Germany

Murat Sağlam
Department Mathematik/Informatik, Abteilung Mathematik Universität zu Köln Köln Germany

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Volume 25, issue 4 (2025)