The Limit Values of the Non-abelian Twisted Reidemeister Torsion Associated to Knots
نویسنده
چکیده
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.
منابع مشابه
Non abelian twisted Reidemeister torsion for fibered knots
In this article, we give an explicit formula to compute the non-abelian twisted sign-determined Reidemeister torsion of the exterior of a fibered knot in terms of its monodromy. As an application, we give explicit formulae for the non abelian Reidemeister torsion of torus knots and of the figure eight knot.
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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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Given a λ-regular SU(2) or SL(2,C)-representation of a knot group, we show a relationship between a zero of acyclic Reidemeister torsion and non-acyclic Reidemeister torsion. Then we can give a method to calculate non-abelian twisted Reidemeister torsion of its knot exterior. We calculate some examples and investigate the behavior of non-abelian SU(2)-twisted Reidemeister torsion associated to ...
متن کاملNon–abelian Reidemeister Torsion for Twist Knots
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متن کاملLimit Values of the Non-acyclic Reidemeister Torsion for Knots
We consider the Reidemeister torsion associated with SL2(C)representations of a knot group. A bifurcation point in the SL2(C)-character variety of a knot group is a character which is given by both an abelian SL2(C)representation and a non-abelian one. We show that there exist limits of the non-acyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivati...
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تاریخ انتشار 2005