AI 中文总结
该研究针对带A_k型拉格朗日球面构型的Liouville域，引入Penner型类概念并证明其Floer理论熵为正，据此构造无穷多具正Floer理论熵的光滑平凡辛同痕类正合辛微分同胚，还证明其Floer理论熵是拓扑熵的下界。
AI 中文摘要
我们引入带有k≥2的拉格朗日球面A_k构型的Liouville域上正合辛微分同胚的Penner型类的概念，证明该类具有正Floer理论熵。作为推论，我们在任何容许A_2型拉格朗日球面构型的4n维Liouville域上，构造出无穷多个具有正Floer理论熵的光滑平凡辛同痕类的正合辛微分同胚。我们还证明，Liouville域上正合辛微分同胚的Floer理论熵为其拓扑熵提供了一个下界。
英文摘要
We introduce the notion of a Penner-type class of an exact symplectomorphism on a Liouville domain with an $A_k$-configuration of Lagrangian spheres for $k\geqslant 2$, and prove that such a class has positive Floer-theoretic entropy. As a corollary, we construct infinitely many smoothly trivial symplectic isotopy classes of exact symplectomorphisms with positive Floer-theoretic entropy on any $4n$-dimensional Liouville domain that admits an $A_2$-configuration of Lagrangian spheres. We also prove that the Floer-theoretic entropy of an exact symplectomorphism on a Liouville domain provides a lower bound for its topological entropy.
Comments29 pages, 7 figures; added references and Remark 1.3
