Representations of Knot Groups and Twisted Alexander Polynomials
نویسنده
چکیده
We present a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.
منابع مشابه
Metabelian representations , twisted Alexander polynomials , knot slicing , and mutation
Given a knot complement X and its p-fold cyclic cover X p → X , we identify twisted polynomials associated to GL1 ( F[t±1] ) representations ofπ1(X p) with twisted polynomials associated to related GL p ( F[t±1] ) representations of π1(X) which factor through metabelian representations. This provides a simpler and faster algorithm to compute these polynomials, allowing us to prove that 16 (of 1...
متن کاملar X iv : 0 80 4 . 13 55 v 1 [ m at h . G T ] 8 A pr 2 00 8 METABELIAN REPRESENTATIONS , TWISTED ALEXANDER POLYNOMIALS , KNOT SLICING , AND MUTATION
Given a knot complement X and its p–fold cyclic cover Xp → X, we identify twisted polynomials associated to GL1(F[t]) representations of π1(Xp) with twisted polynomials associated to related GLp(F[t]) representations of π1(X) which factor through metabelian representations. This provides a simpler and faster algorithm to compute these polynomials, allowing us to prove that 16 (of 18 previously ...
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In this paper we extend several results about classical knot invariants derived from the infinite cyclic cover to the twisted case. Let X be a finite complex with fundamental group n, let o :nPG ̧(») be a linear representation where » is a finite dimensional vector space over a field F, and let e : nPZ be a homomorphism. Finally let X = be the infinite cyclic cover of X corresponding to e. The r...
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