Algebraic & Geometric Topology

Homfly polynomials of generalized Hopf links

Hugh R Morton and Richard J Hadji

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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.

Article information

Source
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 11-32.

Dates
Received: 25 June 2001
Revised: 11 January 2002
Accepted: 11 January 2002
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882682

Digital Object Identifier
doi:10.2140/agt.2002.2.11

Mathematical Reviews number (MathSciNet)
MR1885213

Zentralblatt MATH identifier
1002.57014

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Hopf link satellites reverse parallels Homfly polynomial

Citation

Morton, Hugh R; Hadji, Richard J. Homfly polynomials of generalized Hopf links. Algebr. Geom. Topol. 2 (2002), no. 1, 11--32. doi:10.2140/agt.2002.2.11. https://projecteuclid.org/euclid.agt/1513882682


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References

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