Non-orientable 4-genus of torus knots

Megan Fairchild; Hailey Jay Garcia; Jake Murphy; Hannah Percle

doi:10.1142/s021821652650001x

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arXiv · 2405.04737

Non-orientable 4-genus of torus knots

Megan Fairchild·Hailey Jay Garcia·Jake Murphy·Hannah Percle

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Abstract

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.

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BibTeX RIS

Megan Fairchild, Hailey Jay Garcia, Jake Murphy, Hannah Percle. 2024-05-08. Non-orientable 4-genus of torus knots. https://doi.org/10.1142/s021821652650001x

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