论文标题
扩展在表面上的免费小组动作
Extending free group action on surfaces
论文作者
论文摘要
目前的工作介绍了新的观点，以便将有限的小组动作从表面扩展到3个manifolds。我们考虑与有限的组$ g $相关的Schur乘数在第二个维度的$ g $ $ g $方面，称为$ g $ bobordisms。我们对有限群体在封闭的表面上的自由行动何时延伸到3个manifold上的非本地自由动作的问题感兴趣。我们对这个问题的答案对于阿贝尔，二面，对称和交替的群体是肯定的。作为我们方法的应用，我们表明，在封闭式的表面上，阿贝尔群体（在某些条件下）和二面体组的每个非必要的自由行动都延伸至$ 3 $维二维手柄。
The present work introduces new perspectives in order to extend finite group actions from surfaces to 3-manifolds. We consider the Schur multiplier associated to a finite group $G$ in terms of principal $G$-bordisms in dimension two, called $G$-cobordisms. We are interested in the question of when a free action of a finite group on a closed oriented surface extends to a non-necessarily free action on a 3-manifold. We show the answer to this question is affirmative for abelian, dihedral, symmetric and alternating groups. As an application of our methods, we show that every non-necessarily free action of abelian groups (under certain conditions) and dihedral groups on a closed oriented surface extends to $3$-dimensional handlebody.
