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). pp. 83-103. ISSN 0305-0041, 1469-8064

Text MortonStricklandpreprint.pdf - Unspecified Download (750kB)

Abstract

Results of Kirillov and Reshetikhin on constructing invariants of framed links from the quantum group SU(2)q 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)q-invariant of a link L is a linear combination of Jones polynomials of parallels of L, 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 L and an evaluation of Kauffman’s polynomial for sublinks of L is deduced. © 1991, Cambridge Philosophical Society. All rights reserved.

Item Type:	Article
Uncontrolled Keywords:	Jones polynomial, satellite, knot invariant
Depositing User:	Symplectic Admin
Date Deposited:	26 Jan 2016 09:05
Last Modified:	28 Feb 2026 23:40
DOI:	10.1017/S0305004100069589
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2048519
Disclaimer:	The University of Liverpool is not responsible for content contained on other websites from links within repository metadata. Please contact us if you notice anything that appears incorrect or inappropriate.