关于覆盖的扩张
On extension of coverings
摘要：
我们解决的问题时，覆盖的边界的表面可以扩展到覆盖的表面（相当于：当有一个分支覆盖规定的monodromy）。如果这样的扩展是可能的，那么什么时候可以把全空间看作是连通的呢？什么时候可以把延期视为正常？我们给出了有限覆盖和无限覆盖的充要条件（无限覆盖是我们的主要焦点）。为了证明我们的结果，我们展示了独立兴趣的群论结果，例如Ore}定理的以下扩展（和简化）：无限对称群的每个元素是两个元素的交换子，这两个元素一起传递
英文摘要：
We address the question of when a covering of the boundary of a surface can be extended to a covering of the surface (equivalently: when is there a branched cover with a prescribed monodromy). If such an extension is possible, when can the total space be taken to be connected? When can the extension be taken to be regular? We give necessary and sufficient conditions for both finite and infinite covers (infinite covers are our main focus). In order to prove our results, we show group-theoretic results of independent interests, such as the following extension (and simplification) of the theorem of Ore}: every element of the infinite symmetric group is the commutator of two elements which, together, act transitively
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