3 problems

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The conjecture that signature invariants cannot detect the kernel of the first mutation map
Signature-detection conjecture. In general, signature invariants cannot detect elements in the kernel of $\phi_1$ .
Conjectureopencasson-gordon-invariants knot-concordance mutation-invariantsarXiv posted 2 days ago
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Casson–Gordon signature characterization of ribbon 2-bridge knots
Let $K_{m^2,q}$ be a 2-bridge knot, and let $\mathcal{R}$ denote the family of ribbon knots. The Casson–Gordon signature invariants associated to the double branched cover are the…
Conjectureopen2-bridge-knots casson-gordon-invariants knot-theoryarXiv posted 2 days ago
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Friedl–Powell vanishing conjecture for height 3.5 Whitney tower concordance
A link is height $3.5$ Whitney tower concordant to the Hopf link if it is related to the Hopf link by a height $3.5$ Whitney tower concordance. Friedl and Powell constructed a Cass…
Conjectureopencasson-gordon-invariants link-concordance whitney-towersarXiv posted 2 days ago

The conjecture that signature invariants cannot detect the kernel of the first mutation map