Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 070, 11 pages      arXiv:2410.05846      https://doi.org/10.3842/SIGMA.2025.070

Mikami-Weinstein Type Theorem for Cosymplectic Groupoid Actions

Shuhei Yonehara
National Institute of Technology, Yonago College, Tottori, 683-8502, Japan

Received January 20, 2025, in final form August 06, 2025; Published online August 16, 2025

Abstract
The Mikami-Weinstein theorem is a generalization of the classical Marsden-Weinstein-Meyer symplectic reduction theorem to the case of symplectic groupoid actions. In this paper, we introduce the notion of a cosymplectic groupoid action on a cosymplectic manifold and prove a theorem which is a natural analogue of the Mikami-Weinstein theorem.

Key words: cosymplectic manifolds; cosymplectic groupoids; momentum maps; Hamiltonian actions.

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