Covers of surfaces

Ian Biringer, Yassin Chandran, Tommaso Cremaschi, Jing Tao, Nicholas G. Vlamis, Mujie Wang, Brandis Whitfield
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Abstract

We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal abelian covers and the $\mathbb{Z}/n\mathbb{Z}$-homology covers of surfaces, and we show that non-locally finite characteristic covers of surfaces have four possible homeomorphism types.
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表面覆盖物
我们研究了(总是可定向的)曲面的某些盖的同构类型,通常是无穷型的。我们证明了每一个具有非阿贝尔基群的曲面都被每一个非紧凑曲面所覆盖,我们识别了曲面的普遍非阿贝尔覆盖和$\mathbb{Z}/n\mathbb{Z}$同构覆盖,并证明了曲面的非局部有限特征覆盖有四种可能的同构类型。
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