Algebraic and Geometric Topology 2 (2002), paper no. 2, pages 11-32.

Homfly polynomials of generalized Hopf links

Hugh R. Morton, Richard J. Hadji

Abstract. Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse string satellites of the Hopf link.

Keywords. Hopf link, satellites, reverse parallels, Homfly polynomial

AMS subject classification. Primary: 57M25.

DOI: 10.2140/agt.2002.2.11

E-print: arXiv:math.GT/0106207

Submitted: 25 June 2001. (Revised: 11 January 2002.) Accepted: 11 January 2002. Published: 15 January 2002.

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Hugh R. Morton, Richard J. Hadji
Department of Mathematical Sciences, University of Liverpool
Peach Street, Liverpool, L69 3ZL, UK
Email: morton@liv.ac.uk, rhadji@liv.ac.uk
URL: http://www.liv.ac.uk/~su14/knotgroup.html
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