Twisted Alexander polynomials of plane algebraic curves
نویسندگان
چکیده
منابع مشابه
Alexander-Lin twisted polynomials
X.S. Lin’s original definition of twisted Alexander knot polynomial is generalized for arbitrary finitely presented groups. J. Cha’s fibering obstruction theorem is generalized. The group of a nontrivial virtual knot shown by L. Kauffman to have trivial Jones polynomial is seen also to have a faithful representation that yields a trivial twisted Alexander polynomial.
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— In this paper, we give a brief survey on the fundamental group of the complement of a plane curve and its Alexander polynomial. We also introduce the notion of θ-Alexander polynomials and discuss their basic properties. Résumé (Un état des lieux sur les polynômes d’Alexander des courbes planes) Dans cet article, nous donnons un bref état des lieux sur le groupe fondamental du complémentaire d...
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We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2,C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. ...
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The group of a nontrivial knot admits a finite permutation representation such that the corresponding twisted Alexander polynomial is not a unit.
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The group of a nontrivial knot admits a finite permutation representation such that the corresponding twisted Alexander polynomial is not a unit.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2007
ISSN: 0024-6107
DOI: 10.1112/jlms/jdm004