On the impossibility of a generalization of the HOMFLY — Polynomial to Labelled Oriented Graphs

Antje Christensen; Stephan Rosebrock

Displaying similar documents to “On the impossibility of a generalization of the HOMFLY — Polynomial to Labelled Oriented Graphs”

Combinatorics and topology - François Jaeger's work in knot theory

Louis H. Kauffman (1999)

Annales de l'institut Fourier

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François Jaeger found a number of beautiful connections between combinatorics and the topology of knots and links, culminating in an intricate relationship between link invariants and the Bose-Mesner algebra of an association scheme. This paper gives an introduction to this connection.

On the Alexander polynomials of alternating two-component links.

Kidwell, Mark E. (1979)

International Journal of Mathematics and Mathematical Sciences

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Geometric types of twisted knots

Mohamed Aït-Nouh, Daniel Matignon, Kimihiko Motegi (2006)

Annales mathématiques Blaise Pascal

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Let $K$ be a knot in the $3$ -sphere $S^{3}$ , and $Δ$ a disk in $S^{3}$ meeting $K$ transversely in the interior. For non-triviality we assume that $| Δ \cap K | \geq 2$ over all isotopies of $K$ in $S^{3} - \partial Δ$ . Let $K_{Δ, n}$ ( $\subset S^{3}$ ) be a knot obtained from $K$ by $n$ twistings along the disk $Δ$ . If the original knot is unknotted in $S^{3}$ , we call $K_{Δ, n}$ a . We describe for which pair $(K, Δ)$ and an integer $n$ , the twisted knot $K_{Δ, n}$ is a torus knot, a satellite knot or a hyperbolic knot.

Knots, butterflies and 3-manifolds..

H. M. Hilden, J. M. Montesinos, D. M. Tejada, M. M. Toro (2004)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

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Intrinsic knotting and linking of complete graphs.

Flapan, Erica (2002)

Algebraic & Geometric Topology

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Yamada polynomial and crossing number of spatial graphs.

Tomoe Motohashi, Yoshiyuki Ohyama, Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we estimate the crossing number of a flat vertex graph in 3-space in terms of the reduced degree of its Yamada polynomial.

Basic polyhedra in knot theory

Slavik V. Jablan, Ljiljana M. Radović, Radmila Sazdanović (2005)

Kragujevac Journal of Mathematics

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Links associated with generic immersions of graphs.

Kawamura, Tomomi (2004)

Algebraic & Geometric Topology

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Invariants of piecewise-linear knots

Richard Randell (1998)

Banach Center Publications

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We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.