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Teruaki Kitano, Takayuki Morifuji (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree for a fibered knot of genus .
Garoufalidis, Stavros, Lan, Yueheng (2005)
Algebraic & Geometric Topology
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Kitano, Teruaki, Suzuki, Masaaki, Wada, Masaaki (2005)
Algebraic & Geometric Topology
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Kalfagianni, Efstratia (2004)
Algebraic & Geometric Topology
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Moshe Cohen, Oliver T. Dasbach, Heather M. Russell (2014)
Fundamenta Mathematicae
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We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.
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...
Paweł Traczyk (1995)
Banach Center Publications
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Champanerkar, Abhijit, Kofman, Ilya (2005)
Algebraic & Geometric Topology
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Nafaa Chbili (2003)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Prabhakar Madeti, Rama Mishra (2006)
Fundamenta Mathematicae
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We discuss polynomial representations for 2-bridge knots and determine the minimal degree sequence for all such knots. We apply the connection between rational tangles and 2-bridge knots.