Algebraic & Geometric Topology

Homfly polynomials of generalized Hopf links

Hugh R Morton and Richard J Hadji

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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.

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hopf link satellites reverse parallels Homfly polynomial


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.

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