On a relation between torsion numbers and Alexander matrix of a knot

Madan Lal Mehta

Displaying similar documents to “On a relation between torsion numbers and Alexander matrix of a knot”

Twisted Alexander polynomials and surjectivity of a group homomorphism.

Kitano, Teruaki, Suzuki, Masaaki, Wada, Masaaki (2005)

Algebraic & Geometric Topology

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Divisibility of twisted Alexander polynomials and fibered knots

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 $S L (2, 𝔽)$ -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree $4 g - 2$ for a fibered knot of genus $g$ .

A partial order in the knot table.

Kitano, Teruaki, Suzuki, Masaaki (2005)

Experimental Mathematics

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Positive knots, closed braids and the Jones polynomial

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...

The slicing number of a knot.

Livingston, Charles (2002)

Algebraic & Geometric Topology

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Infinite order amphicheiral knots.

Livingston, Charles (2001)

Algebraic & Geometric Topology

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Lissajous knots and billiard knots

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.

Concordance and mutation.

Kirk, P., Livingston, C. (2001)

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Alexander ideals of classical knots.

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.

Applications of topology to DNA

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.