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Homfly polynomials of generalized Hopf links. (English) Zbl 1002.57014
The generalized Hopf links in question are constructed by replacing each of the two components of a Hopf link by a set of unknotted parallel circles of mixed orientations. To compute their Homfly polynomials, a connection to the skein of the annulus is established, using the skein relations of the framed Homfly polynomial. A key point consists in describing a generalized Hopf link within the skein of the annulus via the endomorphism of the skein generated by adding the bounding circle of a transversal disk to a basic circle of the annulus.

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 20C08 Hecke algebras and their representations
##### Keywords:
tangle; Hecke algebra; Young diagram; HOMFLY polynomial; skein; annulus
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##### References:
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