论文标题
一个无限的编织小组代表家族
An infinite family of braid group representations
论文作者
论文摘要
圆盘上的$ d $ fold（$ d \ geq 3 $）分支覆盖物将编织组的无几何嵌入到映射课程中。 我们在本文中，就自由组的发电机的行动而言，将这些辫子组表示的新的明确表达为自由组的自动形态群体。 我们还提供了一种系统的方式来构建和表达这些辫子组表示，以一个名为“覆盖群体”的新小工具来构建和表达这些辫子。 我们证明，由$ d $ fold覆盖的映射类组中的每个发电机$ \wideTildeβ_i$都是$ d $ fold覆盖的产品，这是$ d-1 $ dehn twings的产物。
The $d$-fold ($d \geq 3$) 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 $\widetildeβ_i$ of braid group inside mapping class group induced by $d$-fold covering is the product of $d-1$ Dehn twists on the surface.
