Non-orientable 4-genus of torus knots
Autor: | Fairchild, Megan, Garcia, Hailey Jay, Murphy, Jake, Percle, Hannah |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | The non-orientable 4-genus of a knot $K$ in $S^{3}$, denoted $\gamma_4(K)$, measures the minimum genus of a non-orientable surface in $B^{4}$ bounded by $K$. We compute bounds for the non-orientable 4-genus of knots $T_{5, q}$ and $T_{6, q}$, extending previous research. Additionally, we provide a generalized, non-recursive formula for $d(S^{3}_{-1}(T_{p,q}))$, the $d$-invariant of -1-surgery on torus knots. Comment: 13 pages, 2 figures, corrected typo in references, added attribution to Lobb for disproving non-orientable analog of Milnor conjecture |
Databáze: | arXiv |
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