arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.00396math.GT
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P纤维编织物的加捻和卫星操作

Twisting and satellite operations on P-fibered braids

Benjamin Bode

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15 pages, 5 figures
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摘要：

几何辫子$B$可以被解释为具有不同根的一元复多项式空间中的环。该循环定义了一个函数$g:\mathbb{C}\times S^1\to\mathbb{C}$，该函数在$B$上消失。我们定义的一组P-纤维编织的辫子，可以表示为多项式的循环，使得相应的功能$g$诱导纤维化$\arg g:(\mathbb{C}\times S^1)\backslash B\to S^1$。我们表明，一定的卫星操作产生新的P-纤维编织从已知的。我们还证明，任何具有$n$链、$k_-$负交叉和$k_+$正交叉的编织物$B$都可以通过向其添加至少$\tfrac{k_-+1}{n}$负或$\tfrac{k_+ +1}{n}$正全扭转而变成P纤维编织物（因此也变成其闭合是纤维编织物）。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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