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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.11952 |
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| _version_ | 1866916668258648064 |
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| author | Carter, J. Scott Choi, Seonmi Kim, Byeorhi |
| author_facet | Carter, J. Scott Choi, Seonmi Kim, Byeorhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Folding Branched Covers of the $3$-Sphere Branched over Knots Carter, J. Scott Choi, Seonmi Kim, Byeorhi Geometric Topology 57K10, 57M12 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. |
| title | Folding Branched Covers of the $3$-Sphere Branched over Knots |
| topic | Geometric Topology 57K10, 57M12 |
| url | https://arxiv.org/abs/2503.11952 |