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

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### 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.

### Most cited references7

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(1979)
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### Inequivalent frame-spun knots with the same complement

(1992)
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### Knot modules and seifert matrices

(1978)
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### Author and article information

###### Journal
2013-02-27
2015-07-07
###### Article
1302.6665