Non-orientable 4-genus of torus knots

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.