Folding Branched Covers of the $3$-Sphere Branched over Knots

J. Scott Carter; Seonmi Choi; Byeorhi Kim

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arXiv · 2503.11952

Folding Branched Covers of the $3$-Sphere Branched over Knots

J. Scott Carter·Seonmi Choi·Byeorhi Kim

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Abstract

A folding of a branched cover of the 3-sphere that is branched over a knot is a continuous map of the cover into the product of the sphere with a disk that has the property that the projection onto the sphere factor induces the covering. Moreover, away from the branch set, the map is a general position immersion. Cyclic branched covers can be folded so that the map is an embedding when the disk factor is 2-dimensional. Dihedral branched covers can also be folded. In as much as possible, the foldings that are presented are quite detailed. In particular, the paper focuses upon a folding of the dihedral cover of the 3-sphere that is branched along a torus knot of type (2,5). The cover also is homeomorphic to the $3$-sphere.

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BibTeX RIS

J. Scott Carter, Seonmi Choi, Byeorhi Kim. 2025-03-15. Folding Branched Covers of the $3$-Sphere Branched over Knots. https://arxiv.org/abs/2503.11952

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