论文标题
P纤维编织物上的扭曲和卫星操作
Twisting and satellite operations on P-fibered braids
论文作者
论文摘要
几何辫子$ b $可以解释为具有独特根部的Monic复合物多项式空间中的循环。此循环定义了一个函数$ g：\ mathbb {c} \ times s^1 \ to \ mathbb {c} $，它消失在$ b $上。我们将一组P纤维辫子定义为可以由多项式循环表示的编织物，以使相应的函数$ g $诱导纤维化$ \ arg g：（\ sathbb {c} \ times s^1）\ backslash backslash b \ to s^1 $。我们表明，某些卫星操作会产生来自已知卫星的新辫子。我们还证明，任何具有$ n $ strands，$ k _- $负数和$ k _+$的辫子$ b $都可以通过添加至少$ \ tfrac {k _--+1} $ $ \ t Twist n+potive of $ n $ strands，$ k _- $ potrands和$ k _- $ potrands和$ k _- $ n $对此。
A geometric braid $B$ can be interpreted as a loop in the space of monic complex polynomials with distinct roots. This loop defines a function $g:\mathbb{C}\times S^1\to\mathbb{C}$ that vanishes on $B$. We define the set of P-fibered braids as those braids that can be represented by loops of polynomials such that the corresponding function $g$ induces a fibration $\arg g:(\mathbb{C}\times S^1)\backslash B\to S^1$. We show that a certain satellite operation produces new P-fibered braids from known ones. We also prove that any braid $B$ with $n$ strands, $k_-$ negative and $k_+$ positive crossings can be turned into a P-fibered braid (and hence also into a braid whose closure is fibered) by adding at least $\tfrac{k_-+1}{n}$ negative or $\tfrac{k_+ +1}{n}$ positive full twists to it.
