Rasmussen s-invariants of satellites do not detect slice knots

On rational sliceness of Miyazaki's fibered, −amphicheiral knots

“…Here, the Q-homology 0-bipolar knot is a Q-homology analog of 0-bipolar knots whose precise definition will be given in Section 3. As noted in [CK15], there are Q-homology 0-bipolar knots which generate a subgroup isomorphic to Z ∞ ⊕ Z ∞ 2 in either the smooth or topological knot concordance groups. In particular, all rationally slice knots are Q-homology 0-bipolar, so their sliceness cannot be detected by the ν + invariant by Theorem 1.7.…”

“…This would give a negative answer to Kawauchi's question. Also inspired by recent work of Cha and the first author [CK15], we like to determine whether the collection of ν + invariants of satellites detects slice knots. More precisely, if ν + (P (K)) = ν + (P (U )) holds for all satellite patterns P ⊂ S 1 × D 2 , does it imply that K is slice?…”