On Farber's invariants for simple \(2q\)-knots

Let \(K\) be a simple \(2q\)-knot with exterior \(X\). We show directly how the Farber quintuple \((A,\Pi,\alpha,\ell,\psi)\) determines the homotopy type of \(X\) if the torsion subgroup of \(A=\pi_q(X)\) has odd order. We comment briefly on the possible role of the EHP sequence in recovering the boundary inclusion from the duality pairings \(\ell \) and \(\psi\). Finally we reformulate the Farber quintuple as an hermitian self-duality of an object in an additive category with involution.