Homfly polynomials of generalized Hopf links (Q5954322)

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.