多项式递推序列的牛顿多边形及其在TQFT中的作用
The Newton polygon of a recurrence sequence of polynomials and its role in TQFT
摘要：
本文包含了一个组合定理（多项式递归序列的牛顿多边形序列是拟线性的）及其在经典拓扑和量子拓扑中的两个应用，即在填充下$A$ -多项式和固定量子不变量（如Jones多项式）的行为。我们的组合定理，补充Calegari-沃克\cite{CW}和作者\cite{Ga4}的结果，占据了大部分的文件，其证明需要Lech-马勒-Skolem定理的$p$ -进解析数论结合多面体和热带几何的基本原理。
英文摘要：
The paper contains a combinatorial theorem (the sequence of Newton polygons of a reccurent sequence of polynomials is quasi-linear) and two applications of it in classical and quantum topology, namely in the behavior of the $A$-polynomial and a fixed quantum invariant (such as the Jones polynomial) under filling. Our combinatorial theorem, which complements results of Calegari-Walker \cite{CW} and the author \cite{Ga4}, occupies the bulk of the paper and its proof requires the Lech-Mahler-Skolem theorem of $p$-adic analytic number theory combined with basic principles in polyhedral and tropical geometry.
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