Non abelian twisted Reidemeister torsion for fibered knots
نویسنده
چکیده
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.
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...
متن کاملThe Relationship between a Zero of Acyclic Reidemeister Torsion and Non Acyclic Reidemeister Torsion
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 ...
متن کاملA Relationship between a Zero of Acyclic Reidemeister Torsion and Non Acyclic Reidemeister Torsion
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 کاملThe Limit Values of the Non-abelian Twisted Reidemeister Torsion Associated to Knots
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.
متن کاملReidemeister Torsion for Linear Representations and Seifert Surgery on Knots
We study an invariant of a 3-manifold which consists of Reidemeister torsion for linear representations which pass through a finite group. We show a Dehn surgery formula on this invariant and compute that of a Seifert manifold over S 2. As a consequence we obtain a necessary condition for a result of Dehn surgery along a knot to be Seifert fibered, which can be applied even in a case where abel...
متن کامل