Vol. 316, No. 2, 2022

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A Serre–Swan theorem for coisotropic algebras

Marvin Dippell, Felix Menke and Stefan Waldmann

Vol. 316 (2022), No. 2, 277–306
Abstract

Coisotropic algebras are used to formalize coisotropic reduction in Poisson geometry and in deformation quantization; they find applications in other fields as well. Here we prove a Serre–Swan theorem relating the regular projective modules over the coisotropic algebra built out of a manifold M, a submanifold C and an integrable smooth distribution D TC with vector bundles over this geometric situation and show an equivalence of categories for the case of a simple distribution.

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Keywords
coisotropic algebra, projective coisotropic module, Serre–Swan theorem, foliation, vector bundles
Mathematical Subject Classification
Primary: 13C10
Secondary: 14D21, 16D40, 53B05, 53C12, 53D17
Milestones
Received: 20 January 2021
Revised: 23 March 2021
Accepted: 25 December 2021
Published: 6 April 2022
Authors
Marvin Dippell
Department of Mathematics
Julius Maximilian University of Würzburg
Würzburg
Germany
Felix Menke
Department of Mathematics
Julius Maximilian University of Würzburg
Würzburg
Germany
Stefan Waldmann
Department of Mathematics
Julius Maximilian University of Würzburg
Würzburg
Germany