论文标题
Boothby-Wang定理用于BESSE接触歧管
A Boothby-Wang theorem for Besse contact manifolds
论文作者
论文摘要
如果其所有轨道都是周期性的，则可能具有不同的时期，则在接触歧管上的Reeb流量称为Besse。我们表征了接触歧管，其reeb流是besse的主要s^1-孔，而在满足某些共同体条件的整体符号符号孔上。除了共同的条件外，该陈述出现在Boyer和Galicki的作品中，以Sasakian几何形状的语言出现。我们说明了一些不常见的视角在上述结果证明的情况下，而没有提及其他结构。更确切地说，我们通过有限的稳定剂组平稳地谎言组的动作作为歧管的商。通过以这种模棱两可的方式引入所有相关的Orbifold概念，我们避免使用Orbifold图表进行修补结构。 作为一个应用程序，并在Cristofaro-Gardiner的工作基础上 - Mazzucchelli，我们推断出封闭的Besse Contact 3-manifolds的完整分类，以严格的接触型。
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.
