Reduction of multisymplectic manifolds

We extend the Marsden-Weinstein-Meyer symplectic reduction theorem to the setting of multisymplectic manifolds. In this context, we investigate the dependence of the reduced space on the reduction parameters. With respect to a distinguished class of multisymplectic moment maps, an exact stationary phase approximation and nonabelian localization theorem are also obtained.

Automated summary

The study extends the Marsden-Weinstein-Meyer symplectic reduction theorem to the context of multisymplectic manifolds, investigating the dependence of the reduced space on the reduction parameters. It also obtains an exact stationary phase approximation and nonabelian localization theorem concerning a distinguished class of multisymplectic moment maps.