Twisted Reidemeister Torsion for Twist Knots
نویسنده
چکیده
A. The aim of this paper is to give an explicit formula for the SL 2(C)-twisted Reidemeister torsion in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables giving approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.
منابع مشابه
Non–abelian Reidemeister Torsion for Twist Knots
Twist knots form a family of special two–bridge knots which include the trefoil knot and the figure eight knot. The knot group of a two–bridge knot has a particularly nice presentation with only two generators and a single relation. One could find our interest in this family of knots in the following facts: first, twist knots except the trefoil knot are hyperbolic; and second, twist knots are n...
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Given a λ-regular SU(2) or SL(2,C)-representation of a knot group, we show how to calculate non-abelian twisted Reidemeister torsion of its knot exterior. This method is due to considering the relationship between a zero of acyclic Reidemeister torsion and non-acyclic Reidemeister torsion. We calculate some examples and investigate the behavior of non-abelian SU(2)-twisted Reidemeister torsion ...
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In math.GT/0510607, a conjecture is suggested by J. Dubois and R. Kashaev. It is that the differential coefficient of the abelian Reidemeister torsion of a knot exterior at a bifurcation point of the SL(2, C)-representation variety of its knot group corresponds a limit value of the non-abelian twisted Reidemeister torsion of the knot exterior. We shall prove this conjecture in the present paper.
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تاریخ انتشار 2007