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Reduction of multisymplectic manifolds

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Abstract

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.

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Acknowledgements

The author would like to thank Manuel de León for helpful comments on an early draft of this paper, and Takuya Sakasai for suggesting the topic of generalized Duistermaat–Heckman theorems. The author would also like to acknowledge the support of the East China Normal University, the China Postdoctoral Science Foundation, and the Euler International Mathematical Institute in Saint Petersburg. This work is supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No075–15–2019–1619.

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  1. Saint Petersburg State University and Leonhard Euler International Mathematical Institute in Saint Petersburg, 14th Line 29B, Vasilyevsky Island, St., Petersburg, 199178, Russia

    Casey Blacker

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Blacker, C. Reduction of multisymplectic manifolds. Lett Math Phys 111, 64 (2021). https://doi.org/10.1007/s11005-021-01408-y

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