关于Besse接触流形的Boothby-Wang定理
A Boothby-Wang theorem for Besse contact manifolds
AI总结：
本文提出关于Besse接触流形的Boothby-Wang定理，通过轨道束理论和上同调条件，对闭合Besse接触3流形进行严格接触同构下的完整分类。
摘要：
一个接触流形上的Reeb流被称为Besse如果其所有轨道都是周期性的，可能具有不同的周期。我们 characterization 那些Reeb流为Besse的接触流形作为主S^1-轨道束，其基底是满足某些上同调条件的积分辛轨道束。除了上同调条件外，这一陈述在Boyer和Galicki的工作中以Sasakian几何的语言出现。我们通过不引用额外结构的方式，在证明上述结果时展示了对轨道束的一些不常见视角。更具体地说，我们通过流形上的光滑李群作用，其稳定化子群为有限群，将轨道束视为商集。通过以这种等变方式引入所有相关的轨道束概念，我们避免了使用轨道束图表的拼接构造。作为应用，基于Cristofaro-Gardiner--Mazzucchelli的工作，我们推导出闭合Besse接触3流形在严格接触同构下的完整分类。
英文摘要：
A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as principal S^1-orbibundles over integral symplectic orbifolds satisfying some cohomological condition. Apart from the cohomological condition this statement appears in the work of Boyer and Galicki in the language of Sasakian geometry. We illustrate some non-commonly dealt with perspective on orbifolds in a proof of the above result without referring to additional structures. More precisely, we work with orbifolds as quotients of manifolds by smooth Lie group actions with finite stabilizer groups. By introducing all relevant orbifold notions in this equivariant way we avoid patching constructions with orbifold charts. As an application, and building on work by Cristofaro-Gardiner--Mazzucchelli, we deduce a complete classification of closed Besse contact 3-manifolds up to strict contactomorphism.
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