Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard symplectic ball, 𝔹2n, implies a rather strict topological condition on the free contact circle actions on the standard contact sphere, 𝕊2n−1. We also prove an analogue for a Liouville domain and contact circle actions on its boundary. Applications include results concerning the symplectic mapping class group and the fundamental group of the group of contactomorphisms.

中文翻译：

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奇异的辛同胚和接触圈动作

使用 Floer 理论方法，我们证明标准辛球上不存在奇异辛同胚，𝔹2n,意味着标准接触球上的自由接触圆动作有一个相当严格的拓扑条件，𝕊2n-1.我们还证明了刘维尔域的类比和在其边界上的接触圆动作。应用包括关于辛映射类群和接触同胚群的基本群的结果。