论文标题
动力滑轮
Dynamical sheaves
论文作者
论文摘要
在目前的工作中，我们定义并研究了任何小型站点$ x $的分类（或“商”）站点$ [x/σ] $，其中包含（可计数）coproducts，并具有（可计数的）半群$σ$。一个简单的情况（与我们的应用程序最相关的情况）是$σ= \ mathbb {n} $的情况，因此，我们集中精力。我们的主要结果包括在$ x $上与``$σ-$ action''建立相应的tòpos等效性。我们还证明，$ [x/\ mathbb {n}] $中有一个频谱序列计算捆绑的共同体，我们推断了该站点的某些拓扑特性，例如其基本组。最终，我们将上述形式主义应用于全态动力学中，从而对爱泼斯坦在Fatou-Shishikura的不平等和无穷小的Thurston的僵化中进行了理论解释。
In the present work we define and study the classifying (or "quotient") site $[X/Σ]$ for any small site $X$ with (countable) coproducts endowed with an action of a (countable) semigroup $Σ$. A simple case (the most relevant to our applications) is the case $Σ=\mathbb{N}$, on which, therefore we concentrate. Our main result consists in establishing an equivalence of the corresponding Tòpos with the category of sheaves on $X$ with ``$Σ-$action''. We prove also that there is a spectral sequence computing sheaf cohomology in $[X/\mathbb{N}]$ and we deduce some topological properties of this site, such as its fundamental group. We finally apply the above formalism in Holomorphic Dynamics, giving a Tòpos-theoretic interpretation of Epstein's work on the Fatou-Shishikura Inequality and Infinitesimal Thurston's Rigidity.
