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Real algebraic links in S3 and braid group actions on the set of n-adic integers
Journal of Knot Theory and Its Ramifications ( IF 0.5 ) Pub Date : 2020-05-20 , DOI: 10.1142/s021821652050039x
Benjamin Bode 1
Affiliation  

We construct an infinite tower of covering spaces over the configuration space of [Formula: see text] distinct nonzero points in the complex plane. This results in an action of the braid group [Formula: see text] on the set of [Formula: see text]-adic integers [Formula: see text] for all natural numbers [Formula: see text]. We study some of the properties of these actions such as continuity and transitivity. The construction of the actions involves a new way of associating to any braid [Formula: see text] an infinite sequence of braids, whose braid types are invariants of [Formula: see text]. We present computations for the cases of [Formula: see text] and [Formula: see text] and use these to show an infinite family of braids close to real algebraic links, i.e. links of isolated singularities of real polynomials [Formula: see text].

中文翻译:

S3 中的实代数链接和 n 进整数集上的编织群动作

我们在[公式:见正文]复平面中不同的非零点的配置空间上构建了一个无限的覆盖空间塔。这导致编织组 [Formula: see text] 对所有自然数 [Formula: see text] 的 [Formula: see text]-adic 整数 [Formula: see text] 的集合的作用。我们研究了这些动作的一些属性,例如连续性和传递性。动作的构建涉及一种新的方法,可以将无限的辫子序列关联到任何辫子 [公式:见文本],其辫子类型是 [公式:见文本] 的不变量。我们对[公式:见文本]和[公式:见文本]的情况进行计算,并使用这些计算来显示接近实代数链接的无限辫子族,即实数多项式的孤立奇点链接[公式:见文本] .
更新日期:2020-05-20
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