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 $(A,Π,α,\ell,ψ)$ determines the homotopy type of $X$ if the torsion subgroup of $A=π_q(X)$ 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 $ψ$. Finally we reformulate the Farber quintuple as an hermitian self-duality of an object in an additive category with involution.

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