## 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.

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