Twisted Alexander polynomials and surjectivity of a group homomorphism.
Kitano, Teruaki, Suzuki, Masaaki, Wada, Masaaki (2005)
Algebraic & Geometric Topology
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Kitano, Teruaki, Suzuki, Masaaki, Wada, Masaaki (2005)
Algebraic & Geometric Topology
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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 .
Kitano, Teruaki, Suzuki, Masaaki (2005)
Experimental Mathematics
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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...
Livingston, Charles (2002)
Algebraic & Geometric Topology
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Livingston, Charles (2001)
Algebraic & Geometric Topology
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Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
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We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
Kirk, P., Livingston, C. (2001)
Geometry & Topology
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Cherry Kearton, Stephen M. J. Wilson (1997)
Publicacions Matemàtiques
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The Alexander ideals of classical knots are characterised, a result which extends to certain higher dimensional knots.
Isabel Darcy, De Sumners (1998)
Banach Center Publications
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The following is an expository article meant to give a simplified introduction to applications of topology to DNA.