Jones polynomial invariants for knots and satellites



Morton, HR ORCID: 0000-0002-8524-2695 and Strickland, P
(1991) Jones polynomial invariants for knots and satellites. Mathematical Proceedings of the Cambridge Philosophical Society, 109 (1). 83 - 103.

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Abstract

<jats:title>Abstract</jats:title><jats:p>Results of Kirillov and Reshetikhin on constructing invariants of framed links from the quantum group SU(2)<jats:sub><jats:italic>q</jats:italic></jats:sub> are adapted to give a simple formula relating the invariants for a satellite link to those of the companion and pattern links used in its construction. The special case of parallel links is treated first. It is shown as a consequence that any SU(2)<jats:sup><jats:italic>q</jats:italic></jats:sup>-invariant of a link <jats:italic>L</jats:italic> is a linear combination of Jones polynomials of parallels of <jats:italic>L</jats:italic>, where the combination is determined explicitly from the representation ring of SU(2). As a simple illustration Yamada's relation between the Jones polynomial of the 2-parallel of <jats:italic>L</jats:italic> and an evaluation of Kauffman's polynomial for sublinks of <jats:italic>L</jats:italic> is deduced.</jats:p>

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 26 Jan 2016 09:05
Last Modified: 09 Aug 2021 11:09
DOI: 10.1017/s0305004100069589
URI: https://livrepository.liverpool.ac.uk/id/eprint/2048519

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