TWISTED ALEXANDER INVARIANTS OF TWISTED LINKS
نویسندگان
چکیده
منابع مشابه
Twisted Alexander Invariants of Twisted Links
Let L = 1∪· · ·∪ d+1 be an oriented link in S3, and let L(q) be the d-component link 1 ∪· · ·∪ d regarded in the homology 3-sphere that results from performing 1/q-surgery on d+1. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.
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Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We can show that the invariants coincide with signdetermined Reidemeister torsion in a normalized setting and refine the duality theorem. As an application, we obtain stronger necessary co...
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The Pontryagin dual of the twisted Alexander module for a dcomponent link and GLNZ representation is an algebraic dynamical system with an elementary description in terms of colorings of a diagram. In the case of a knot, its associated topological entropy is the logarithmic growth rate of the number of torsion elements in the twisted first-homology group of r-fold cyclic covers of the knot comp...
متن کاملOn Reciprocality of Twisted Alexander Invariants
Given a knot and an SLnC 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 SL3Z representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal.
متن کاملFibred Knots and Twisted Alexander Invariants
We study the twisted Alexander invariants of fibred knots. We establish necessary conditions on the twisted Alexander invariants for a knot to be fibred, and develop a practical method to compute the twisted Alexander invariants from the homotopy type of a monodromy. It is illustrated that the twisted Alexander invariants carry more information on fibredness than the classical Alexander invaria...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2012
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216512501180