论文标题
在福卡亚类别上的符号畸形和P-ADIC分析作用的迭代
Iterations of symplectomorphisms and p-adic analytic actions on the Fukaya category
论文作者
论文摘要
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 $ϕ$ isotopic to the identity.可以将这个家庭视为福卡亚类别上的$ P $ -ADIC分析行动。使用此情况，我们推断出浮动共同体学组的等级$ hf（ϕ^k（l），l';λ）$在\ mathbb {z} $中$ k \ in \ k \ in \ kathbb {z} $都是常数，并且有限许多例外。我们还证明了一个类似的结果，没有通过在这种情况下显示如何构建P-ADIC分析作用的通用$ ϕ $同位素对身份的单调性假设。我们将应用于分类熵和Seidel的猜想。
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.
