余辛同构群同构意味着流形微分同构
Isomorphism of cosymplectomorphism groups implies diffeomorphism of manifolds
AI总结：
余辛同构群同构性可推导出流形的微分同构性，通过分析Reeb流与映射筒的共轭类保持性。
摘要：
我们证明，如果两个闭合、连通、正则的余辛流形具有同构的余辛同构群（作为拓扑群），则其底层流形是微分同构的。证明过程通过将Reeb流作为群的中心，并将同构降维到辛基流形。我们显示同构保持映射筒的共轭类，从而确保束结构以及总空间等价。
英文摘要：
We prove that if two closed, connected, regular cosymplectic manifolds have isomorphic groups of cosymplectomorphisms (as topological groups), then the underlying manifolds are diffeomorphic. The proof proceeds by characterizing the Reeb flow as the center of the group and descending the isomorphism to the symplectic base manifolds. We show that the isomorphism preserves the conjugacy class of the monodromy of the mapping torus, which ensures that the bundle structures, and thus the total spaces are equivalent.
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