There are oriented 2-knots with isomorphic fundamental groups, semilinearly isomorphic second homotopy modules, and isomorphic quandles, but inequivalent first Postnikov invariants.
H., The Derived Module of a Homomorphism, Advances in Mathematics, vol
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Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots
There are oriented 2-knots with isomorphic fundamental groups, semilinearly isomorphic second homotopy modules, and isomorphic quandles, but inequivalent first Postnikov invariants.