Displaying similar documents to “The classification of partially symmetric 3-braid links”

Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics

Józef Przytycki (1995)

Banach Center Publications

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We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, taken from the graph theory, the third, invented by Jones, transplants into knot theory the idea of the Yang-Baxter equation with the spectral parameter (idea employed by Baxter in the theory of solvable models in statistical...

Quasipositivity and new knot invariants.

Lee Rudolph (1989)

Revista Matemática de la Universidad Complutense de Madrid

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This is a survey (including new results) of relations ?some emergent, others established? among three notions which the 1980s saw introduced into knot theory: quasipositivity of a link, the enhanced Milnor number of a fibered link, and the new link polynomials. The Seifert form fails to determine these invariants; perhaps there exists an ?enhanced Seifert form? which does.

Brunnian links

Paul Gartside, Sina Greenwood (2007)

Fundamenta Mathematicae

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A Brunnian link is a set of n linked loops such that every proper sublink is trivial. Simple Brunnian links have a natural algebraic representation. This is used to determine the form, length and number of minimal simple Brunnian links. Braids are used to investigate when two algebraic words represent equivalent simple Brunnian links that differ only in the arrangement of the component loops.

On polynomials and surfaces of variously positive links

Alexander Stoimenow (2005)

Journal of the European Mathematical Society

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It is known that the minimal degree of the Jones polynomial of a positive knot is equal to its genus, and the minimal coefficient is 1, with a similar relation for links. We extend this result to almost positive links and partly identify the next three coefficients for special types of positive links. We also give counterexamples to the Jones polynomial-ribbon genus conjectures for a quasipositive knot. Then we show that the Alexander polynomial completely detects the minimal genus and...

Homfly polynomials as vassiliev link invariants

Taizo Kanenobu, Yasuyuki Miyazawa (1998)

Banach Center Publications

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We prove that the number of linearly independent Vassiliev invariants for an r-component link of order n, which derived from the HOMFLY polynomial, is greater than or equal to min{n,[(n+r-1)/2]}.