Non-orientable 4-genus of torus knots
| Autor: | Fairchild, Megan, Garcia, Hailey Jay, Murphy, Jake, Percle, Hannah |
|---|---|
| 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 |
| Externí odkaz: |
|