The Non-Orientable 4-Genus of 11 Crossing Non-Alternating Knots
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916144913317888 |
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| author | Fairchild, Megan |
| author_facet | Fairchild, Megan |
| contents | The non-orientable 4-genus of a knot K in the three sphere is defined to be the minimum first Betti number of a non-orientable surface F in the four-ball so that K bounds F. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We also will view obstructions to a knot bounding a Möbius band given by the double branched cover of the three sphere branched over K. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Non-Orientable 4-Genus of 11 Crossing Non-Alternating Knots Fairchild, Megan Geometric Topology Algebraic Topology The non-orientable 4-genus of a knot K in the three sphere is defined to be the minimum first Betti number of a non-orientable surface F in the four-ball so that K bounds F. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We also will view obstructions to a knot bounding a Möbius band given by the double branched cover of the three sphere branched over K. |
| title | The Non-Orientable 4-Genus of 11 Crossing Non-Alternating Knots |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2403.00996 |