论文标题
将表面的周期性自动形态扩展到3个manifolds
Extending periodic automorphisms of surfaces to 3-manifolds
论文作者
论文摘要
令$ g $为一个有限的组，在连接的紧凑型表面$σ$上作用，而$ m $是整数同源性3-Sphere。我们表明，如果相对于固定嵌入$σ\ rightarrow m $，$ g $的每个元素都可以超过$ m $，那么$ g $在$ m $ 1统治的一些$ m'$上是可扩展的。从这个结果中，在可定向类别中，我们对3个球体上可扩展的封闭表面的所有周期性自动形态进行了分类。这种自动形态的相应嵌入式表面始终是Heegaard表面。
Let $G$ be a finite group acting on a connected compact surface $Σ$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $Σ\rightarrow M$, then $G$ is extendable over some $M'$ which is 1-dominated by $M$. From this result, in the orientable category we classify all periodic automorphisms of closed surfaces that are extendable over the 3-sphere. The corresponding embedded surface of such an automorphism can always be a Heegaard surface.
