Floer-Theoretic Entropy of Exact Symplectomorphisms

We introduce the notion of a Penner-type class of an exact symplectomorphism on a Liouville domain with an Ak-configuration of Lagrangian spheres for k⩾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 A2-configuration of Lagrangian spheres. The talk is based on work joint with Myenggi Kwon.