Displaying similar documents to “On polynomials and surfaces of variously positive links”

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.

The classification of partially symmetric 3-braid links

Alexander Stoimenov (2015)

Open Mathematics

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We classify 3-braid links which are amphicheiral as unoriented links, including a new proof of Birman- Menasco’s result for the (orientedly) amphicheiral 3-braid links. Then we classify the partially invertible 3-braid links.

Parity biquandle

Aaron Kaestner, Louis H. Kauffman (2014)

Banach Center Publications

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We use crossing parity to construct a generalization of biquandles for virtual knots which we call parity biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. We find all parity biquandles arising from the Alexander biquandle and quaternionic biquandles. For a particular construction named the z-parity Alexander biquandle we show that the associated polynomial yields a lower bound on the number of odd crossings as well as...

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...