Iterations of symplectomorphisms and p-adic analytic actions on the Fukaya category

• 成果类型: Article
• 署名作者: Kartal, Yusuf Baris
• 署名单位: University of Edinburgh
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01308-7
• 发表日期: 2025
• 页码: 801-864
• 关键词: homological mirror symmetry

摘要

Inspired by the work of Bell on the dynamical Mordell-Lang conjecture, and by family Floer cohomology, we construct p-adic analytic families of bimodules on the Fukaya category of a monotone or negatively monotone symplectic manifold, interpolating the bimodules corresponding to iterates of a symplectomorphism f isotopic to the identity. This family can be thought of as a p-adic analytic action on the Fukaya category. Using this, we deduce that the ranks of the Floer cohomology groups HF(phi k(L),L ';Lambda) are constant in k is an element of Z, with finitely many possible exceptions. We also prove an analogous result without the monotonicity assumption for generic f isotopic to the identity by showing how to construct a p-adic analytic action in this case. We give applications to categorical entropy and a conjecture of Seidel.