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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2008.08566 |
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Table of Contents:
- 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 $ϕ$ 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 $HF(ϕ^k(L),L';Λ)$ are constant in $k\in\mathbb{Z}$, with finitely many possible exceptions. We also prove an analogous result without the monotonicity assumption for generic $ϕ$ 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.