论文标题
从编织组到映射课程组
From braid groups to mapping class groups
论文作者
论文摘要
在本文中，我们将$ n $ strands的辫子组的同态分类为$ g $ surface属的映射类小组。特别是，我们表明当$ g <n-2 $时，所有表示都是循环或标准的。我们的结果很敏锐，从某种意义上说，当出现$ g = n-2 $时，出现了过椭圆形表示的概括，这不是循环或标准的。这给出了在复合面的配置空间上的表面束分类。作为推论，我们部分恢复了Aramayona-Souto的结果，Aramayona-Souto对映射班级组之间的同态分类，并有所改善。
In this paper, we classify homomorphisms from the braid group of $n$ strands to the mapping class group of a genus $g$ surface. In particular, we show that when $g<n-2$, all representations are either cyclic or standard. Our result is sharp in the sense that when $g=n-2$, a generalization of the hyperelliptic representation appears, which is not cyclic or standard. This gives a classification of surface bundles over the configuration space of the complex plane. As a corollary, we partially recover the result of Aramayona-Souto, which classifies homomorphisms between mapping class groups, with a slight improvement.
