On reciprocality of twisted Alexander invariants

Daniel S. Silver (University of South Alabama); Jonathan A. Hillman (University of Sydney); Susan G. Williams (University of South Alabama)

arxiv: 0905.2574 · v1 · pith:C6Q4RNQRnew · submitted 2009-05-15 · 🧮 math.GT

On reciprocality of twisted Alexander invariants

Jonathan A. Hillman (University of Sydney) , Daniel S. Silver (University of South Alabama) , Susan G. Williams (University of South Alabama) This is my paper

classification 🧮 math.GT

keywords representationtwistedconjugatedualgivengroupknotreciprocal

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Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal.

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On reciprocality of twisted Alexander invariants

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