### Alexander polynomial, finite type invariants and volume of hyperbolic knots.

Kalfagianni, Efstratia (2004)

Algebraic & Geometric Topology

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Kalfagianni, Efstratia (2004)

Algebraic & Geometric Topology

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Hikami, Kazuhiro (2003)

Experimental Mathematics

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Livingston, Charles (2002)

Algebraic & Geometric Topology

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Motegi, Kimihiko, Song, Hyun-Jong (2005)

Algebraic & Geometric Topology

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Livingston, Charles (2004)

Algebraic & Geometric Topology

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Friedl, Stefan, Teichner, Peter (2005)

Geometry & Topology

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Alexander Stoimenow (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Using the recent Gauß diagram formulas for Vassiliev invariants of Polyak-Viro-Fiedler and combining these formulas with the Bennequin inequality, we prove several inequalities for positive knots relating their Vassiliev invariants, genus and degrees of the Jones polynomial. As a consequence, we prove that for any of the polynomials of Alexander/Conway, Jones, HOMFLY, Brandt-Lickorish-Millett-Ho and Kauffman there are only finitely many positive knots with the same polynomial and no...

Melvin, Paul, Shrestha, Sumana (2005)

Geometry & Topology

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Anh T. Tran (2015)

Fundamenta Mathematicae

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We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.

Ng, Lenhard L. (2001)

Algebraic & Geometric Topology

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Yasutaka Nakanishi (1996)

Revista Matemática de la Universidad Complutense de Madrid

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This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.

Dean, John C. (2003)

Algebraic & Geometric Topology

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