The [Formula: see text]-fold ([Formula: see text]) branched coverings on a disk give an infinite family of nongeometric embeddings of braid groups into mapping class groups. We, in this paper, give new explicit expressions of these braid group representations into automorphism groups of free groups in terms of the actions on the generators of free groups. We also give a systematic way of constructing and expressing these braid group representations in terms of a new gadget, called covering groupoid. We prove that each generator [Formula: see text] of braid group inside mapping class group induced by [Formula: see text]-fold covering is the product of [Formula: see text] Dehn twists on the surface.

中文翻译：

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自由群的自同构群中的无限编织群表示族

磁盘上的 [Formula: see text]-fold ([Formula: see text]) 分支覆盖将编织组的无限族非几何嵌入到映射类组中。在本文中，我们根据对自由群生成器的作用，将这些辫状群表示新的显式表达为自由群的自同构群。我们还提供了一种系统的方法来构建和表达这些编织组表示，该方法称为覆盖 groupoid。我们证明了[公式：见文本]-折叠覆盖所诱导的映射类群内编织组的每个生成器[公式：见文本]是[公式：见文本] Dehn 在曲面上扭曲的乘积。