On Farber's invariants for simple $2q$-knots

Abstract

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.