On Farber's invariants for simple 2q-knots

Jonathan A. Hillman

Abstract

Let K be a simple 2q-knot with exterior X. We show directly how the Farber quintuple (A,Π,α,l,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 pairings l and ψ. Finally we reformulate the Farber quintuple as an hermitean self-duality of an object in an additive category with involution.

Keywords: EHP sequence, Farber quintuple, F-form, hermitean duality, simple knot.

AMS Subject Classification: Primary 57Q45.