论文标题
双政治PCF多项式的完整性和瑟斯顿刚度
Integrality and Thurston Rigidity for Bicritical PCF Polynomials
论文作者
论文摘要
我们给出一个代数证明，证明瑟斯顿刚性对在某些轻度假设下具有周期性临界点的两次pcf多项式的重要结果。关键结果是，当使用动力学的belyi多项式参数化两项式多项式的家族时，PCF解决方案在某些特殊的素数中是不可或缺的，我们将其称为“指数无数次数的素数”。我们证明，除了一定的情况下，除了一定的情况下，索引除外的素质都有很多列表，并且列出了许多例外情况。然后将这些素数用于证明横向性。
We give an algebraic proof of an important consequence of Thurston rigidity for bicritical PCF polynomials with periodic critical points under certain mild assumptions. The key result is that when the family of bicritical polynomials is parametrized using dynamical Belyi polynomials, the PCF solutions are integral at certain special primes, which we term ``index divisor free primes.'' We prove the existence of index divisor free primes in all but finitely many cases and conjecture the complete list of exceptions. These primes are then used to prove transversality.
