标题： Thurston Vanishing 显示英文标题

标题： Thurston Vanishing

摘要： 我们展示如何将Epstein的有理映射$f$的代数横截性原理${\mathbb P}^1_{\mathbb C}$扩展到Fatou集的无限前向不变子集。 至少在概念上，做到这一点的关键是拥有一个$f$不变层的拓扑，以及在其中Grothendieck的六个运算，Epstein的理论自然发生在此处。 因此，得到的非排斥不变循环的计数严格优于Epstein和Shishikura的最小值。 顺便（在抛物固定点上函子地应用Epstein/Thurston方法）我们计算了一个实爆破的对偶层，这是一个非常代数的对象，具有独立的兴趣，能够极大地简化重生函数和Stokes现象的理论。 显示英文摘要

摘要： We show how to extend Epstein's algebraic transversality principles for rational maps $f$ of ${\mathbb P}^1_{\mathbb C}$ to infinite forward invariant subsets of the Fatou set. The key, at least conceptually, to doing this is to have a topos of $f$ invariant sheaves, and Grothendieck's six operations on the same in which Epstein's theory naturally takes place. Thus the resulting count of non-repelling invariant cycles is strictly better than the minimum of Epstein and Shishikura. En passant (in functorially applying the Epstein/Thurston methodology at parabolic fixed points) we calculate the dualising sheaf of a real blow up which is a remarkably algebraic object of independent interest with the capacity to enormously simplify the theory of resurgent functions and Stokes' phenomenon.