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Homfly polynomials of
generalized Hopf links
Hugh R Morton and Richard J Hadji |
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Algebraic & Geometric Topology 2 (2002) 11–32
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arXiv: math.GT/0106207 |
Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 57M25
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References |
Forward citations |
Publication
Received: 25 June 2001
Revised: 11 January 2002
Accepted: 11 January 2002
Published: 15 January 2002
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Authors |
| Hugh R Morton | |
| Department of Mathematical
Sciences University of Liverpool Peach Street Liverpool L69 3ZL UK |
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| http://www.liv.ac.uk/~su14/knotgroup.htm | |
| Richard J Hadji | |
| Department of Mathematical
Sciences University of Liverpool Peach Street Liverpool L69 3ZL UK |
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