论文标题
模棱两可的映射课程组和轨道辫子组
Equivariant Mapping Class Group and Orbit Braid Group
论文作者
论文摘要
由伯曼（Birman）关于映射课程组和辫子小组之间关系的工作的动机，我们讨论了轨道辫子群体与封闭式$ m $上的典范映射班级组之间的关系，并在本文中进行了免费且适当的群体行动。我们的构造基于纤维化$ \ MATHCAL {f} _ {0}^{g} m \ rightarrow f（m/g，n）$给出的确切序列。结论与商的编织组密切相关。与没有组动作的情况相比，当商空间为$ \ mathbb {t}^{2} $时，会有很大的区别。
Motivated by the work of Birman about the relationship between mapping class groups and braid groups, we discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface $M$ with a free and proper group action in this article. Our construction is based on the exact sequence given by the fibration $\mathcal{F}_{0}^{G}M \rightarrow F(M/G,n)$. The conclusion is closely connected with the braid group of the quotient space. Comparing with the situation without the group action, there is a big difference when the quotient space is $\mathbb{T}^{2}$.
