A Serre–Swan theorem for coisotropic algebras

Marvin Dippell, Felix Menke and Stefan Waldmann

Vol. 316 (2022), No. 2, 277–306

DOI: 10.2140/pjm.2022.316.277

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 $D\subseteq TC$ with vector bundles over this geometric situation and show an equivalence of categories for the case of a simple distribution.

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