Whitehead Doubles and Non-Orientable Surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929561040584704 |
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| author | Fairchild, Megan |
| author_facet | Fairchild, Megan |
| contents | Whitehead doubles provide a plethora of examples of knots that are topologically slice but not smoothly slice. We discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used techniques to obstructing sliceness. Additionally, we improve bounds in general for the non-orientable 4 genus of $t$-twisted Whitehead doubles and provide genus 1 non-orientable cobordisms to cable knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Whitehead Doubles and Non-Orientable Surfaces Fairchild, Megan Geometric Topology Whitehead doubles provide a plethora of examples of knots that are topologically slice but not smoothly slice. We discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used techniques to obstructing sliceness. Additionally, we improve bounds in general for the non-orientable 4 genus of $t$-twisted Whitehead doubles and provide genus 1 non-orientable cobordisms to cable knots. |
| title | Whitehead Doubles and Non-Orientable Surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2410.13736 |