Reduction theory for singular symplectic manifolds and singular forms on moduli spaces

© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license
The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [25,21, 28] for b-symplectic manifolds and [12,14] for folded symplec-tic manifolds). However, reduction theory has not been set in this realm in full generality. This is fundamental, among other reasons, to advance in the “quantization commutes with reduction” programme for these manifolds initiated in [29,30].
The project that gave rise to these results received the support of a fellowship from “la Caixa” Foundation (ID 100010434) under the INPHINIT 2018 program for excellence centers. The grant is attached to the retained excellence project Interactions between symmetries and singularities in Geometry and Physics supervised by Eva Miranda. The fellowship code is LCF/BQ/DI18/11660046. Anastasia Matveeva and Eva Miranda are partially supported by the Spanish State Research Agency, through the grant PID2019-103849GB-I00 of AEI /10.13039/501100011033
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