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arXiv · 2409.03967

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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Ian Biringer, Yassin Chandran, Tommaso Cremaschi, Jing Tao, Nicholas G. Vlamis, Mujie Wang, Brandis Whitfield. 2025-08-03. Covers of surfaces. https://arxiv.org/abs/2409.03967

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