Relationship between the kauffman bracket polynomials of torus knots: (T3,3n+1) and (T3,3n+2)

dc.contributor.authorDissanayake, A.A.A.W.N.
dc.contributor.authorAlmeida, S.V.A.
dc.date.accessioned2024-01-09T09:09:18Z
dc.date.available2024-01-09T09:09:18Z
dc.date.issued2023
dc.description.abstractKnot theory is a branch of topology that studies mathematical knots. New knot invariants were the foundation for the work of many mathematicians. A knot invariant is a property 􀟙 for a knot 􀜭, where 􀟙 is the same for any projection of 􀜭. A knot polynomial is one such knot invariant. Knot polynomials are polynomials that are assigned to knot projections based on the mathematical properties of the knots. This study is restricted to polynomials of torus knots, knots that lie on an unknotted torus, without crossing over or under themselves as they lie on the torus. Every torus knot is a (􀝌, 􀝍)-torus knot, where 􀝌 and 􀝍 are two relatively prime integers that are represented by the symbol 􀜶􀯣,􀯤. Most of the research done on this particular area of Knot Theory, has focused on finding polynomial representations such as Kauffman Bracket polynomial, the Bracket polynomial for the (2, 􀝍)-torus knot and polynomial representations such as Alexander polynomial, Conway polynomial and Jones polynomial for the (􀝌, 􀝍)-torus knot. With the exception of the complete solution to the Alexander, Conway, and Jones polynomials of 􀜶􀯣,􀯤, the problem of determining the polynomial for 􀜶􀬶,􀯤 is almost solved. The study is an attempt to solve the computation problem for the Kaufmann Bracket Polynomial of 􀜶􀯣,􀯤. The work will provide a relationship between Kauffman Bracket polynomials of the torus knots’ 􀵫􀜶􀬷,􀬷􀯡􀬾􀬶􀵯 and 􀵫􀜶􀬷,􀬷􀯡􀬾􀬵􀵯 for 􀝊 􀗐􀜰.en_US
dc.identifier.citationDissanayake A.A.A.W.N.; Almeida S.V.A. (2023), Relationship between the kauffman bracket polynomials of torus knots: (T3,3n+1) and (T3,3n+2), proceedings of the postgraduate institute of Science Research Congress, postgraduate institute of Science Research Congress, Sri Lankaen_US
dc.identifier.urihttp://repository.kln.ac.lk/handle/123456789/27174
dc.publisherFaculty of Science, University of Kelaniya Sri Lankaen_US
dc.subjectKnot invariants, Knot polynomials, Skein relations, Torus knotsen_US
dc.titleRelationship between the kauffman bracket polynomials of torus knots: (T3,3n+1) and (T3,3n+2)en_US

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