Knot Cabling and the Degree of the Colored Jones Polynomial

dc.contributor.authorKalfagianni, E.en_US
dc.contributor.authorTran, Anh T.en_US
dc.contributor.utdAuthorTran, Anh T.en_US
dc.date.accessioned2016-07-07T16:45:35Z
dc.date.available2016-07-07T16:45:35Z
dc.date.created2015-09-16en_US
dc.date.issued2015-09-16en_US
dc.description.abstractWe study the behavior of the degree of the colored Jones polynomial and the boundary slopes of knots under the operation of cabling. We show that, under certain hypothesis on this degree, if a knot K satisfies the Slope Conjecture then a (p, q)-cable of K satisfies the conjecture, provided that p/q is not a Jones slope of K. As an application we prove the Slope Conjecture for iterated cables of adequate knots and for iterated torus knots. Furthermore we show that, for these knots, the degree of the colored Jones polynomial also determines the topology of a surface that satisfies the Slope Conjecture. We also state a conjecture suggesting a topological interpretation of the linear terms of the degree of the colored Jones polynomial (Conjecture 5.1), and we prove it for the following classes of knots: iterated torus knots and iterated cables of adequate knots, iterated cables of several nonalternating knots with up to nine crossings, pretzel knots of type (-2, 3, p) and their cables, and two-fusion knots.en_US
dc.description.sponsorshipE. K. was partially supported in part by NSF grants DMS{1105843 and DMS{1404754.en_US
dc.identifier.bibliographicCitationKalfagianni, E., and A. T. Tran. 2015. "Knot cabling and the degree of the colored Jones polynomial." New York Journal of Mathematics 21, retrieved from http://nyjm.albany.edu/j/2015/21-41.htmlen_US
dc.identifier.issn1076-9803en_US
dc.identifier.urihttp://hdl.handle.net/10735.1/4920
dc.identifier.volume21en_US
dc.language.isoenen_US
dc.publisherUniversity at Albanyen_US
dc.relation.urihttp://nyjm.albany.edu/j/2015/21-41.html
dc.rights©2015 University of Albany. All rights reseerved.en_US
dc.sourceNew York Journal of Mathematics
dc.subjectAdequate knotsen_US
dc.subjectSatellite knotsen_US
dc.subjectCable knotsen_US
dc.subjectJones polynomialsen_US
dc.titleKnot Cabling and the Degree of the Colored Jones Polynomialen_US
dc.type.genreArticleen_US

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