On the slice-torus invariant $q_M$ from ${\mathbb{Z}}_2$-equivariant Seiberg--Witten Floer cohomology

We show that Iida–Taniguchi’s $\mathbb{Z}$-valued slice-torus invariant $q_M$ cannot be realized as a linear combination of Rasmussen’s $s$-invariant, Ozsváth–Szabó’s $\tau$-invariant, all of the ${\mathfrak{s}\mathfrak{l}}_N$-concordance invariants ($N\ge 2$), Baldwin–Sivek’s instanton $\tau$-invariant, Daemi–Imori–Sato–Scaduto–Taniguchi’s instanton $\tilde{s}$-invariant and Sano–Sato’s Rasmussen type invariants ${\widetilde{ss}}_c$.