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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.

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          Quadratic and hermitian forms in additive and abelian categories

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            Inequivalent frame-spun knots with the same complement

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              Knot modules and seifert matrices

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                Author and article information

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

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Rev. Roumaine Math. Pures Appl. 60 (2015), 405--422
                v2. Minor reorganization and corrections to final section
                math.GT

                Geometry & Topology

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