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arXiv · 2408.12557

Three-Dimensional Small Covers and Links

Vladimir Gorchakov
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Abstract

We study certain orientation-preserving involutions on three-dimensional small covers. We prove that the quotient space of an orientable three-dimensional small cover by such an involution in $\mathbb{Z}_2^3$ is homeomorphic to a connected sum of copies of $S^2 \times S^1$. If this quotient space is a 3-sphere, then the corresponding small cover is a two-fold branched covering of the 3-sphere along a link. We provide a description of this link in terms of the polytope and the characteristic function.

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Vladimir Gorchakov. 2024-08-22. Three-Dimensional Small Covers and Links. https://arxiv.org/abs/2408.12557

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