Non-orientable 4-genus of torus knots

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 $d(S_{-1}^3(T_{p,q}))$, the $d$-invariant of -1-surgery on torus knots.

13 pages, 2 figures, corrected typo in references, added attribution to Lobb for disproving non-orientable analog of Milnor conjecture

References in corpus (5)

• Concordance homomorphisms from knot Floer homology
• On cobordisms between knots, braid index, and the Upsilon-invariant
• The nonorientable four-genus of knots
• The non-orientable 4-genus for knots with 8 or 9 crossings
• On the nonorientable four-ball genus of torus knots