Let M be a manifold with a geometric structure and sufficiently nice G a symmetry group, often the geometric structure can be transferred to M/G. In (multi-)symplectic geometry, reduction procedures permit to transfer the differential form to an even smaller space. However, all approaches working directly on the space have very strong regularity requirements. We present an approach to reducing the algebra of (multi-)symplectic observables for general (covariant) moment maps, without any regularity assumptions of the level sets (and the symmetries). Even in the well-studied symplectic case, this construction is distinct from pre-existing ones. Based on joint work with Casey Blacker.

1. C. Blacker, Reduction of multisymplectic manifolds, Lett. Math. Phys., 2021, https://doi.org/10.1007/s11005-021-01408-y
2. C. Blacker, A. Miti & L. Ryvkin, Reduction of L_∞-algebras of observables on multisymplectic manifolds, Submitted, 2022, https://arxiv.org/abs/2206.03137
3. A. Miti & L. Ryvkin, Constraint observable algebras, (in preparation).