Geodesic
On polynomials and surfaces of variously positive links
Journal of the European Mathematical Society, Tome 7 (2005) no. 4, pp. 477-509

Voir la notice de l'article provenant de la source EMS Press

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 3 following 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 fiber property of canonical Seifert surfaces associated to almost positive (and almost alternating) link diagrams.
DOI : 10.4171/jems/36
Classification : 57-XX, 00-XX
Keywords: positive link, quasipositive link, almost positive link, almost alternating link, Alexander polynomial, Jones polynomial, fiber surface, ribbon genus 
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     author = {Alexander Stoimenow},
     title = {On polynomials and surfaces of variously positive links},
     journal = {Journal of the European Mathematical Society},
     pages = {477--509},
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     year = {2005},
     doi = {10.4171/jems/36},
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Alexander Stoimenow. On polynomials and surfaces of variously positive links. Journal of the European Mathematical Society, Tome 7 (2005) no. 4, pp. 477-509. doi: 10.4171/jems/36

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