46 research outputs found

    Finiteness of the image of the Reidemeister torsion of a splice

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    The set RT(M)\mathit{RT}(M) of values of the SL(2,C)\mathit{SL}(2,\mathbb{C})-Reidemeister torsion of a 3-manifold MM can be both finite and infinite. We prove that RT(M)\mathit{RT}(M) is a finite set if MM is the splice of two certain knots in the 3-sphere. The proof is based on an observation on the character varieties and AA-polynomials of knots.Comment: 16 pages, 1 figure, to appear in Ann. Math. Blaise Pasca

    Twisted Alexander polynomials and a partial order on the set of prime knots

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    We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.Comment: This is the version published by Geometry & Topology Monographs on 25 February 200

    Twisted Alexander polynomials and surjectivity of a group homomorphism

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    If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain knot groups.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-51.abs.htm
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