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).
pp. 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 |
|---|---|
| Uncontrolled Keywords: | Jones polynomial, satellite, knot invariant |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 26 Jan 2016 09:05 |
| Last Modified: | 15 Dec 2022 07:34 |
| DOI: | 10.1017/S0305004100069589 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/2048519 |
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