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

Abstract

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 $\ddot{I}„$-invariant, all of the ${\mathfrak{sl}}_N$-concordance invariants ($N\ge 2$), Baldwin--Sivek's instanton $\ddot{I}„$-invariant, Daemi--Imori--Sato--Scaduto--Taniguchi's instanton $\tilde{s}$-invariant and Sano--Sato's Rasmussen type invariants ${\widetilde{ss}}_c$.

14 pages, 3 figures