Homfly Polynomials of Generalized Hopf Links

Details Homfly Polynomials of Generalized Hopf Links Homfly Polynomials of Generalized Hopf Links

2001-06-25

arxiv.org/abs/math/0106207v2

Algebr. Geom. Topol. 2 (2002) 11-32

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-2.abs.html

Scientific paper

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.

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