Bennequin-Plamenevskaya-Shumakovitch type inequalities for Kronheimer-Mrowka's concordance invariant

We give Bennequin-Plamenevskaya-Shumakovich type lower bounds for the concordance invariant $s^{\mathrm{\#}}$ introduced by Kronheimer and Mrowka. The proof is a consequence of computations for torus knots and the cobordism inequality of $s^{\mathrm{\#}}$ due to Gong, combined with well-known arguments used for slice-torus invariants.